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How do you solve $4 x^{2} - 6 = - 12 x$ $4x^2-6=-12x$ ?

1 Answer

Dec 27, 2016

$x = \frac{- 3 \pm \sqrt{15}}{2}$ $x=(-3+-sqrt(15))/2$

Explanation:

$4 x^{2} - 6 = 12 x$ $4x^2-6=12x$

$\to 4 x^{2} + 12 x - 6 = 0$ $rarr 4x^2+12x-6=0$

$\to 2 x^{2} + 6 x - 3 = 0$ $rarr 2x^2+6x-3=0$

applying the quadratic formula:
$XXX x = \frac{- 6 \pm \sqrt{6^{2} - 4 \cdot 2 \cdot (- 3)}}{2 \cdot 2}$ $color(white)("XXX")x=(-6+-sqrt(6^2-4 * 2 * (-3)))/(2 * 2)$

$XXX = \frac{- 6 \pm \sqrt{36 + 24}}{4}$ $color(white)("XXX")=(-6+-sqrt(36+24))/4$

$color(white)("XXX")=(-cancel(6)^3+-cancel(2)sqrt(15))/(cancel(4)_2)$

You could use a calculator if you needed this in an approximate decimal form:
$color(white)("XXX")(-3+-sqrt(15))/2~~0.43691673 or -3.436491673$

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