Question

solve the equation ( x^2 + 8x - 20 = 0 ).
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( x^2 + 8x = square )
( x^2 + 8x + square = square )
( (square)^2 = 36 )
( x + 4 = square )

Explanation:

Step1: Rearrange the equation

$x^2 + 8x = 20$

Step2: Complete the square

$x^2 + 8x + 16 = 20 + 16$

Step3: Rewrite as squared binomial

$(x + 4)^2 = 36$

Step4: Solve for $x+4$

$x + 4 = \pm 6$

Answer:

$x^2 + 8x = \boldsymbol{20}$
$x^2 + 8x + \boldsymbol{16} = \boldsymbol{36}$
$(\boldsymbol{x + 4})^2 = 36$
$x + 4 = \boldsymbol{\pm 6}$

The full solutions for $x$ are $x=2$ and $x=-10$ (derived from $x=6-4$ and $x=-6-4$)