How do you solve $3 x^{2} - 15 x + 18 = 0$ $3x^2 - 15x + 18 = 0$ using the quadratic formula?

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How do you solve $3 x^{2} - 15 x + 18 = 0$ $3x^2 - 15x + 18 = 0$ using the quadratic formula?

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Answer 1 · 2016-07-10T15:45:41

The answers are $x = 2, 3$ $x = 2, 3$ .

Explanation:

The quadratic formula is:

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2} a$ $x = (-b +- sqrt(b^2 - 4ac))/2a$

And in your polynomial:
$a = 3$ $a = 3$
$b = - 15$ $b = -15$
$c = 18$ $c = 18$

So plugging those in we get:

$x = \frac{15 \pm \sqrt{15^{2} - 4 \cdot 3 \cdot 18}}{2 \cdot 3}$ $x = (15 +- sqrt(15^2 - 4*3*18))/(2*3)$
$= \frac{15 \pm \sqrt{225 - 216}}{6}$ $= (15 +- sqrt(225 - 216))/6$
$= \frac{15 \pm \sqrt{9}}{6}$ $= (15 +- sqrt(9))/6$
$= \frac{15 \pm 3}{6}$ $= (15 +- 3)/6$

So our two answers are:

$x = \frac{15 - 3}{6} = \frac{12}{6} = 2$ $x = (15 - 3)/6 = 12/6 = 2$
and
$x = \frac{15 + 3}{6} = \frac{18}{6} = 3$ $x = (15 + 3)/6 = 18/6 = 3$

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How do you solve $3 x^{2} - 15 x + 18 = 0$ $3x^2 - 15x + 18 = 0$ using the quadratic formula?

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How do you solve $3 x^{2} - 15 x + 18 = 0$ $3x^2 - 15x + 18 = 0$ using the quadratic formula?