How do you solve using the completing the square method $x^{2} + \frac{5}{2} x = 5$ $x^2+5/2x=5$ ?

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How do you solve using the completing the square method $x^{2} + \frac{5}{2} x = 5$ $x^2+5/2x=5$ ?

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Answer 1 · 2018-03-03T06:39:14

$x = 1.3117, - 3.8117$ $color(blue)(x = 1.3117, -3.8117$

Explanation:

$x^{2} + (\frac{5}{2}) x = 5$ $x^2 + (5/2)x = 5$

Add ${(\frac{5}{4})}^{2}$ $(5/4)^2$ to both sides

$x^{2} + (\frac{5}{2}) x + {(\frac{5}{4})}^{2} = 5 + {(\frac{5}{4})}^{2}$ $x^2 + (5/2)x + (5/4)^2 = 5 + (5/4)^2$

${(x + (\frac{5}{4}))}^{2} = 5 + (\frac{25}{16}) = \frac{105}{16} = {\sqrt{(\frac{105}{16})}}^{2}$ $(x + (5/4))^2 = 5 + (25/16) = 105/16 = sqrt((105/16))^2$

$(x + (\frac{5}{4})) = \pm \sqrt{\frac{105}{16}}$ $(x + (5/4)) = +-sqrt(105/16)$

$x = \pm (\sqrt{\frac{105}{16}} - (\frac{5}{4}))$ $x = +- (sqrt(105/16) - (5/4))$

$x = 1.3117, - 3.8117$ $x = 1.3117, -3.8117$

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1 Answer

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