# How do you solve x^2 - 6x + 9 = 25?

$x = - 2 , 8$

#### Explanation:

${x}^{2} - 6 x + 9 = 25$

${x}^{2} - 6 x - 16 = 0$

${x}^{2} - 8 x + 2 x - 16 = 0$

$x \left(x - 8\right) + 2 \left(x - 8\right) = 0$

$\left(x - 8\right) \left(x + 2\right) = 0$

$x - 8 = 0 , x + 2 = 0$

$x = 8 , x = - 2$

$x = - 2 , 8$

Jul 9, 2018

$x = - 2 \text{ or } x = 8$

#### Explanation:

$\text{subtract 25 from both sides}$

${x}^{2} - 6 x - 16 = 0 \leftarrow \textcolor{b l u e}{\text{in standard form}}$

$\text{the factors of "-16" which sum to } - 6$
$\text{are "-8" and } + 2$

$\left(x - 8\right) \left(x + 2\right) = 0$

$\text{equate each factor to zero and solve for } x$

$x + 2 = 0 \Rightarrow x = - 2$

$x - 8 = 0 \Rightarrow x = 8$

Jul 16, 2018

$x = 8$ and $x = - 2$

#### Explanation:

Since we have a quadratic, let's set it equal to zero to find its zeroes. This can be done by subtracting $25$ from both sides.

We now have

${x}^{2} - 6 x - 16 = 0$

To factor this, let's do a little thought experiment:

What two numbers sum up to $- 6$ and have a product of $- 16$? After some trial and error, we arrive at $- 8$ and $2$.

This means we can factor this as

$\left(x - 8\right) \left(x + 2\right) = 0$

Setting both factors equal to zero, we get

$x = 8$ and $x = - 2$

Hope this helps!

Jul 16, 2018

$x = 8 \text{ }$ or $\text{ } x = - 2$

#### Explanation:

Given:

${x}^{2} - 6 x + 9 = 25$

Note that both the left hand side and the right hand side are perfect squares, namely:

${\left(x - 3\right)}^{2} = {5}^{2}$

Hence:

$x - 3 = \pm 5$

So:

$x = 3 \pm 5$

That is:

$x = 8 \text{ }$ or $\text{ } x = - 2$