Question

x²+x-90=0 using completing the square method
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Answer 1

Answer:

x = - 10, x = 9

Step-by-step explanation:

Given

x² + x - 90 = 0 ( add 90 to both sides )

x² + x = 90

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2($\frac{1}{2}$ )x + $\frac{1}{4}$ = 90 + $\frac{1}{4}$

(x + $\frac{1}{2}$ )² = $\frac{361}{4}$ ( take the square root of both sides )

x + $\frac{1}{2}$ = ± $\sqrt{\frac{361}{4} }$ = ± $\frac{19}{2}$ ( subtract $\frac{1}{2}$ from both sides )

x = - $\frac{1}{2}$ ± $\frac{19}{2}$ , thus

x = - $\frac{1}{2}$ - $\frac{19}{2}$ = $\frac{-20}{2}$ = - 10

x = - $\frac{1}{2}$ + $\frac{19}{2}$ = $\frac{18}{2}$ = 9