# How do you factor and solve x^2-16=6x?

Feb 11, 2017

$x = - 2 , 8$

#### Explanation:

1) Rearrange into the form$\text{ } a {x}^{2} + b x + c = 0$

2) Factorise

3) Put each bracket $= 0$ and solve each bracket

1) Rearrange

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

subtract $6 x$ from both sides

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

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

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

2) Factorise

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

a) "because it is an " x^2 " equation, the brackets will be of the form " (x+-" ")(x+-" ")

we now need to find the two numbers for the brackets.

${x}^{2} \textcolor{red}{- 6} x \textcolor{b l u e}{- 16} = 0$

we need two numbers that multiply to $\textcolor{b l u e}{- 16}$, but add to $\textcolor{red}{- 6}$

by trial and error:

$- 16 \times 1 = - 16 \implies - 16 + 1 = - 15 \text{ X}$

-8xx2=-16=>-8+ 2=--6" sqrt

so the brackets now become;

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

3) Solve

$x - 8 = 0 \implies x = 8$

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

$\therefore x = - 2 , 8$