Question

Solve x2 + 8x = 33 by completing the square. Which is the solution set of the equation? {–11, 3} {–3, 11} {–4, 4} {–7, 7}

Answer 1

ANSWER
$x = - 11\: or \: x = 3$



EXPLANATION

The quadratic equation given to us is

${x}^{2} + 8x = 33$


We add half the square of the coefficient of
$x$
to both sides of the equation to obtain,

${x}^{2} + 8x + {(4)}^{2} = 33 + {(4)}^{2}$


This implies that,
${x}^{2} + 8x + {(4)}^{2} = 33 + 16$

The right hand side simplifies to

${x}^{2} + 8x + {(4)}^{2} = 49$


The left hand side is a perfect square.

This gives us


${(x + 4)}^{2} = 49$

We take the square root of both sides


$x + 4 = \pm \sqrt{49}$

This evaluates to

$x + 4 = \pm 7$


We make x the subject.


$x = - 4\pm 7$

We now split the square root sign to get



.

$x = - 4 - 7 \: or \: x = - 4 + 7$


$x = - 11\: or \: x = 3$

The correct answer is A.