By completing the scare.
I need a little help with where I’m going wrong, I have the answer but I’m doing something wrong with my signs and keep coming up with the wrong answer. The goal is to “solve by completing the square”
a-2. a+2. a^2 -32.
—— - —— = ——————.
a+2. a-1. a^2 +a-2.
My attempt to clear the fraction:
(a-2)(a-1) - (a+2)(a+2) = a^2 -32
a^2 -a-2a+2-a^2 +2a+2a+4=a^2 -32
-a^2 +a+38=0 (my wrong answer)
The book solution is: a^2 +7a-30=0
Suppose one of the roots of the quadratic equation x^2 + 6ax + b = 0 is √ (3 + √8). If a and b are rational numbers, what is the value of 15ab?
The question was:
(2x – 1)² = (2x + 1)²
Then I did this: 4x² + 1 – 4x = 4x² + 1 + 4x
Now comes the steps where I'm not sure about.
I eliminated the similar "terms" (4x² + 1) on both sides:
–4x = 4x
So I thought that there's no way a Negative X can equal a positive X unless:
X=0
The last two steps were the ones I wasn't sure about so please tell me if I made any mistakes
For projectile questions, is using the quadratic equation allowed to get the time. (using s=ut+1/2at^2)
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Best regards,
Scott
Is there a general solution or a general way to solve equation in the form ax² + bx(1- x²) ½ + cx + d = 0?
f(x)=x^4 - 4x^3 + 10
i know that in order to use the quadratic formula i need to have the first x to the power 2, how can i reduce the power of this equation in the simplist way?
i looked up the internet and they said smth about newton-raphson equation, but i am not so much familar with it
I recently picked up math again and got a little stuck on how to think around factoring trinomials and how to use it to solve quadratic equations. The funny thing is, most of the times I try to google math theory, the explanations are often really bad (imo) and they usually just give you a formula/method without explaining probably the most important thing, WHY it works (the best way to remember). I wanted to leave this here for anyone who is struggling, to save you some time! This might be very basic for some and in that case, please add any tips you got.
So to factor a quadratic equation like -4x^(2) + 18x - 20 = 0 we don't necessarily need to understand the theory behind it, but it's way better if we do. Let's assign the uppercase variables to the numbers excluding any constants and exponents: A = -4, B = 18 and C = -20. We will use uppercase A, B and C for the same places here for any trinomial ax^(2) + bx^(2) + c, where A = a, B = b and C = c.
Usually you will see an explanation like this:
- Find two numbers a & b (lowercase), that adds up to B(18) and at the same time, the product of these numbers should be equal to AC (-4 * -20).
- Of course it is 10 and 8, let's move on. Factor it...
- Answer is x = 2 OR x = 5 / 2, GOOD JOB!
So wtf just happened? And why does step one work?
Before answering the second question, let's do the solution STEP by STEP:
Our equation: -4x^(2) + 18x - 20 = 0
First Step: Find two numbers a & b (lowercase), that adds up to B(18) and at the same time, the product of these numbers should be equal to AC (-4 * -20) = 80... Let's think about this:
B = a + b = 18
AC = a * b = 80
What two numbers sums up to 18 and at the same time multiples to 80? We can try to break it down by finding factors of 80 until we find two factors that also adds up to 18.
80 * 1 = 80
40 * 2 = 80
20 * 4 = 80
10 * 8 = 80 WAIT, isn't 10 + 8 = 18 = B????
Yes sir/ma'am/whatever, you are correct!
Let's break out the coefficient from B(18x) to form the two numbers we just found. The reason we are doing this is because then we can place them into two separate parentheses and find the GCF - greatest common factor for every parentheses.
-4x^(2) + 10x + 8x - 20 = 0
OR
-4x^(2) + (10 + 8)x - 20 = 0
Let's start with -4x^(2) + 10x, what is the GCF here? Actually in this case it's 2x, because we can break out x and 2 from both terms and put it outside the parentheses.
Now we hav
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I never told you why I did it. I'm sure you can guess. Trauma, abuse, stress. I tell you that it feels like catharsis - and it's true - it's why I didn't hesitate that night you asked it of me. There's something so damn thrilling in that moment of painful autonomy. It's a strangled cry of freedom that I yell into the void... until the tickling sensation on my skin brings me back. Did you notice how focused I was in that moment? There was nothing and no one else but you and I.
But… it's about so much more than the singular moment. It's about the reminder, it's about looking at myself and knowing what moment is forever affixed to that scar. It's about the way it feels when I run my hands across my dress and I feel that minor spike of pain. It's an echo of my cry that remains, trapped inside my skin.
But there were times when it wasn't about the things I mentioned above. It wasn't so simple as 'I think of math and I seek an escape'. No. It was more than that. I let my fears grow into a demon - one that scares me more than you do, in a lot of ways. I resigned myself to letting it trample through my psyche, with all of those small marks on my skin drawn as escape routes on a map. The demon never left.
And yet here you are, occupying the same space. You're more real, far more terrifying (if I'm not in the grasp of panic from being overwhelmed by it). You offer me something other people have tried before. Some simply prodded me to hit the books. One sat by my side and worked with me through the problems. I gave up over and over. They got sick of bringing it up, and I got sick of trying. It died on the vine and reinforced my position that I couldn't succeed at this.
I would have never asked for your help with this. I couldn't. Even now, I'm terrified for that future. If anyone can arm me to slay this demon, it would be you. When it's done, I'll present the head of the beast and my blade at your feet and find my place among them.
Forgive me for this mess. I'm trying but I just can't express… how much your guidance means to me. I just can't.
Hey all, I'm having some trouble solving these quadratic polynomial equations for my physics class. Solving with the -b ± (sqrt) b^2 - 4ac /2a has never been my strong suit but my entire homework paper is using this one equation and I'm at a loss. If possible, can you work through the problem [x^2 +2x-7=0] as example? I've already tried solving it myself to no avail.
For which values of k is one solution of 4x^2 - 15x + 4k^3 = 0 square of other solution.
I understand that this is quadratic equation and I know how to find the value of parameter if the solutions need to be same for example but I am not sure how to find the parameter value for this one.
I would like some help and if possible explanation so I can do similar thing myself next time.
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