Question #20bba

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Answer 1 · 2016-11-08T23:41:29

$x = - \frac{1}{2}$ $x=-1/2$ and $x = - \frac{3}{2}$ $x=-3/2$

Solve using the quadratic formula: $4 x^{2} + 8 x = - 3$ $4x^2+8x=-3$

To use the quadratic formula, the equation must be in the form
$a x^{2} + b x + c = 0$ $ax^2+bx+c=0$

Add 3 to both sides to get all the terms on the left.

$4 x^{2} + 8 x a a a = - 3$ $4x^2+8xcolor(white)(aaa)=-3$
$a a a a a a a + 3 a a a + 3$ $color(white)(aaaaaaa)+3color(white)(aaa)+3$

$4 x^{2} + 8 x + 3 = 0$ $color(red)4x^2+color(blue)8x+color(magenta)3=0$

$a = 4, b = 8, c = 3$ $color(red)a=color(red)4, color(blue)b=color(blue)8, color(magenta)c=color(magenta)3$

The quadratic formula is

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x=frac{-color(blue)b+-sqrt(color(blue)b^2-4color(red)acolor(magenta)c)}{2color(red)a}$

$x = \frac{- 8 \pm \sqrt{8^{2} - 4 (4) (3)}}{2 (4)}$ $x=frac{-color(blue)8+-sqrt(color(blue)(8)^2-4(color(red)4)(color(magenta)3))}{2(color(red)4)}$

$x = \frac{- 8 \pm \sqrt{64 - 48}}{8}$ $x=frac{-8+-sqrt(64-48)}{8}$

$x = \frac{- 8 \pm \sqrt{16}}{8}$ $x=frac{-8+-sqrt(16)}{8}$

$x = \frac{- 8 \pm 4}{8}$ $x=(-8+-4)/8$

Separate into two equations, one with a plus in the numerator and the other with a minus.

$x = \frac{- 8 + 4}{8} a a a a x = \frac{- 8 - 4}{8}$ $x=(-8+4)/8color(white)(aaaa)x=(-8-4)/8$

$x = \frac{- 4}{8} a a a a a a a x = \frac{- 12}{8}$ $x=(-4)/8color(white)(aaaaaaa)x=(-12)/8$

$x = - \frac{1}{2} a a a a a a a a x = - \frac{3}{2}$ $x=-1/2color(white)(aaaaaaaa)x=-3/2$