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How do you solve using the completing the square method $x^{2} = 2 x + 4$ $x^2 = 2x + 4$ ?

1 Answer

Oct 26, 2017

$x = 3.236 or x = - 1.236$ $x = 3.236" "or" "x=-1.236$

Explanation:

In the equation $x^{2} - 2 x - 4 = 0$ $x^2 -2x-4=0$ , $- 4$ $" "-4$ is not ${(\frac{b}{2})}^{2}$ $(b/2)^2$

$x^{2} - 2 x = 4 \leftarrow$ $x^2 -2x " "=4" "larr$ move $- 4$ $-4$ to the right side

Add ${(\frac{b}{2})}^{2}$ $color(blue)((b/2)^2)$ to both sides ${(\frac{- 2}{2})}^{2} = 1$ $color(blue)( ((-2)/2)^2 =1)$

$x^{2} - 2 x + 1 = 4 + 1$ $x^2 -2x color(blue)(+1)=4color(blue)(+1)$

${(x - 1)}^{2} = 5$ $" "(x-1)^2 =5$

$x - 1 = \pm \sqrt{5}$ $" "x-1 = +-sqrt5$

$x = + \sqrt{5} + 1 \times \times \times or x = - \sqrt{5} + 1$ $" "x = +sqrt5+1color(white)(xxxxxx) or x = -sqrt5+1$

$x = + \sqrt{5} + 1 \times \times \times or x = - \sqrt{5} + 1$ $" "x = +sqrt5+1color(white)(xxxxxx) or x = -sqrt5+1$

$x = 3.236 or x = - 1.236$ $x = 3.236" "or" "x=-1.236$

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