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}`