How do you solve by completing the square: $x^{2} + 2 x - 24 = 0$ $x^2 +2x - 24 =0$ ?

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How do you solve by completing the square: $x^{2} + 2 x - 24 = 0$ $x^2 +2x - 24 =0$ ?

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Answer 1 · 2015-04-03T01:26:52

Ad $24$ $24$ to both sides to clear the constant from the left side of the equation
$x^{2} + 2 x = 24$ $x^2 + 2x = 24$

Remember that ${(x + 1)}^{2} = x^{2} + 2 x + 1$ $(x+1)^2 = x^2 + 2x +1$
so add $1$ $1$ to both sides in order to complete the square on the left side
$x^{2} + 2 x + 1 = 24 + 1$ $x^2+2x+1 = 24 +1$

${(x + 1)}^{2} = 25$ $(x+1)^2 = 25$

Take the square root of both sides
$x + 1 = \pm 5$ $x+1= +-5$

Giving the solutions
$x = 4$ $x= 4$ and $x = - 6$ $x=-6$

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How do you solve by completing the square: $x^{2} + 2 x - 24 = 0$ $x^2 +2x - 24 =0$ ?

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