Question

Solve by completing the square

Answer 1

$\qquad\qquad\huge\underline{{\sf Answer}}☂$

Let's solve ~

$\qquad \sf \dashrightarrow \: {x}^{2} + 8x = 33$

$\qquad \sf \dashrightarrow \: {x}^{2} + 8x +16 = 33 + 16$

$\qquad \sf \dashrightarrow \: (x + 4) {}^{2} = 49$

$\qquad \sf \dashrightarrow \: x + 4 = \sqrt{49}$

$\qquad \sf \dashrightarrow \: x + 4 = \pm7$

Hence, there are two solutions ~

• 1. when x + 4 = 7

$\qquad \sf \dashrightarrow \: x + 4 = 7$

$\qquad \sf \dashrightarrow \: x = 7 - 4$

$\qquad \sf \dashrightarrow \: x = 3$

• 2. when x + 4 = -7

$\qquad \sf \dashrightarrow \: x + 4 = - 7$

$\qquad \sf \dashrightarrow \: x = - 7 - 4$

$\qquad \sf \dashrightarrow \: x = - 11$

I hope you understood ~