Question

13) Solve the following quadratic equations by completing the square: a) x^2- 12x = 11 b) x² +16x +5=0

Answer 1

we have

$x^2-12x=11$

we have the the trinomial perfect square formula is

$a^2+2ab+b^2$

we have

a=x

2xb=-12x

b=-12x/2x

b=-6

the trinomial square perfect need to be

$x^2-12x+36=0$

we need to add +36 and subtract -36

$x^2-12x+36-36=11$$x^2-12x+36=11+36$$(x-6)^2=47$

then we can factorize

$\mleft(x-6\mright)^2=47$

then we need to isolate x

$x-6=\pm\sqrt[]{47}$

the values of x are

$\begin{gathered} x_1=6+\sqrt[]{47} \\ x_2=6-\sqrt[]{47} \end{gathered}$