Question

Simplify:
(i) $x^2-6x=27$
(ii) $x^2+6x-10=0$

Answer 1

Part $\left(i\right)$

$x^2-6x=27$

Here $a=1,b=-6$ and $c=-27$

Therefore using Quadratic Formula, we get,

$\Rightarrow x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\Rightarrow x=\frac{6\pm \sqrt{36+108}}{2}$

$\Rightarrow x=\frac{6\pm \sqrt{144}}{2}$

$\Rightarrow x=\frac{6\pm 12}{2}$

$\Rightarrow x=\frac{6+12}{2}$ or $\frac{6-12}{2}$

$\Rightarrow x=9$ or $-3$

Part $\left(ii\right)$

$x^2+6x-10=0$

Here $a=1,b=6$ and $c=-10$

Therefore using Quadratic Formula, we get,

$\Rightarrow x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\Rightarrow x=\frac{-6\pm \sqrt{6^2-4\times 1\times -10}}{2\times 1}$

$\Rightarrow x=\frac{-6\pm \sqrt{36+40}}{2}$

$\Rightarrow x=\frac{-6\pm \sqrt{76}}{2}$

$\Rightarrow x=\frac{-6\pm \sqrt{19\times 4}}{2}$

$\Rightarrow x=\frac{-6\pm 2\sqrt{19}}{2}$

$\Rightarrow x=-3\pm \sqrt{19}$

$\Rightarrow x=-3+\sqrt{19}$ or $-3-\sqrt{19}$

Hence, this is the answer.