How do you solve using completing the square method $-3x^2+30x-74$ ?

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How do you solve using completing the square method $-3x^2+30x-74$ ?

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Answer 1 · 2016-08-05T21:27:43

This cannot really be "solved" because it is not an equation and it is not "equal" to anything. It can only be written in a different form.

Answer 2 · 2016-08-05T21:39:05

I got:

$y = -3(x - 5)^2 + 1$

You have:

$y = -3x^2 + 30x - 74$

What you can start with is to make the $x^2$ term have a perfect-square coefficient ( $1$ is fine). That makes it easier to come up with a factor.

Then, halve the $x$ term's coefficient and square it, adding it to both sides.

$y/3 = -x^2 + 10x - 74/3$ (divide by 3)

$-y/3 = x^2 - 10x + 74/3$ (switch signs)

Half of $-10$ is $-5$ , squared is $+25$ . To make common denominators happen, $25 = 75/3$ . Now add it to both sides.

$=> -y/3 + 75/3 = x^2 - 10x + 74/3 + 75/3$

$=> -y/3 = x^2 - 10x + 75/3 - 1/3$

$=> -y/3 = color(green)(x^2 - 10x + 25) - 1/3$

$=> -y/3 = color(green)((x - 5)^2) - 1/3$

Now you can return it back to $y$ by reversing the two things we did in the first steps:

$=> y/3 = -(x - 5)^2 + 1/3$

$=> color(blue)(y = -3(x - 5)^2 + 1)$

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How do you solve using completing the square method $-3x^2+30x-74$ ?

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