How do you solve $2 x^{2} + 9 x = 8$ $2x^2 + 9x = 8$ ?

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How do you solve $2 x^{2} + 9 x = 8$ $2x^2 + 9x = 8$ ?

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Answer 1 · 2016-03-17T10:33:58

Re-write the n equation in standard form then apply the quadratic formula

Explanation:

General standard form for a quadratic:
$XXX a x^{2} + b x + c = 0$ $color(white)("XXX")color(red)(a)x^2+color(blue)(b)x+color(green)(c)=0$
Quadratic formula for roots:
$XXX x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $color(white)("XXX")x=(-color(blue)(b)+-sqrt(color(blue)(b)^2-4color(red)(a)color(green)(c)))/(2color(red)(a))$

$2 x^{2} + 9 x = 8$ $2x^2+9x=8$
expressed in standard form:
$XXX 2 x^{2} + 9 + (- 8) = 0$ $color(white)("XXX")color(red)(2)x^2+color(blue)(9)+color(green)((-8))=0$

Solutions:
$XXX x = \frac{- 9 \pm \sqrt{9^{2} - 4 (2) (- 8)}}{2 (2)}$ $color(white)("XXX")x=(-color(blue)(9)+-sqrt(color(blue)(9)^2-4(color(red)(2))(color(green)(-8))))/(2(color(red)(2)))$

$XXXx = \frac{- 9 \pm \sqrt{145}}{4}$ $color(white)("XXXx")=(-9+-sqrt(145))/4$

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How do you solve $2 x^{2} + 9 x = 8$ $2x^2 + 9x = 8$ ?

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