How do you solve the equation $3 x^{2} - 150 = - 282$ $3x^2-150=-282$ ?

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Answer 1 · 2017-06-02T21:20:30

No real solution

Complex solutions: $x = \pm 2 \sqrt{11} i$ $x = +- 2sqrt(11) i$

Given: $3 x^{2} - 150 = - 282$ $3x^2 - 150 = -282$

Start by adding $282$ $282$ to both sides of the equation: $3 x^{2} - 150 + 282 = 0$ $3x^2 - 150 + 282 = 0$

$3 x^{2} + 132 = 0$ $3x^2 + 132 = 0$

Factor the greatest common factor (GCF) of $3$ $3$ :

$3 (x^{2} + 44) = 0$ $3(x^2 +44) = 0$

If you divide both sides by $3$ $3$ you get:

$x^{2} + 44 = 0$ $x^2 + 44 = 0$

$x^{2} = - 44$ $x^2 = -44$

When you square root both sides you will get a negative value which yields a complex solution since $\sqrt{- 1} = i$ $sqrt(-1) = i$ :

$x = \pm \sqrt{- 44} = \pm 2 \sqrt{- 11} = \pm 2 \sqrt{11} i$ $x = +-sqrt(-44) = +- 2 sqrt(-11) = +- 2sqrt(11) i$

No real solution.

How do you solve the equation 3x2−150=−2823x^2-150=-282?