Question

solve the following by completing square method

x²+8x-11=0​

Answer 1

Answer:

    x² + 8x - 11 = 0

⇒ x² + 8x = 11

⇒ x² + 8x + 4² = 11 + 4²              ( use 4 because it is 8/2 )

⇒ ( x + 4 )² = 11 + 16 = 27

⇒ x + 4 = ±√27 = ±3√3

⇒ x = -4 ± 3√3

Hope that helps!

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:x=-4\pm\sqrt{27}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies {x}^{2} +8x -11 = 0 \\ \\ \red{\underline \bold{to \: find:}} \\ \tt: \implies value \: of \: x =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {x}^{2} +8x -11= 0 \\ \\ \text{Adding \: both \: side }\:\tt(\frac{b}{2a} )^{2} = (\frac{8}{2} )^{2} = \frac{64}{4}=16 \\ \\ \tt: \implies {x}^{2} +8x +16-11= 16 \\ \\ \tt: \implies {(x + 4)}^{2} = 16+ 11\\ \\ \tt: \implies {(x+4)}^{2} = 27 \\ \\ \tt: \implies {x +4} = \sqrt{27} \\ \\ \tt: \implies x +4 = \pm\sqrt{27} \\ \\ \tt: \implies x = \pm \sqrt{27} -4 \\ \\ \green{\tt: \implies x = -4\pm\sqrt{27}}$