How do you solve $x^{2} - 175 = 0$ $x^2-175=0$ using the quadratic formula?

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How do you solve $x^{2} - 175 = 0$ $x^2-175=0$ using the quadratic formula?

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Answer 1 · 2016-07-25T13:18:03

$x = \pm 5 \sqrt{7}$ $x=+-5sqrt(7)$

Explanation:

The quadratic formula for an equation in the form:
$XXX a x^{2} + b x + c = 0$ $color(white)("XXX")color(red)(a)x^2color(blue)(+b)x+color(green)(c)=0$
gives us the solutions:
$XXX x = \frac{- b \pm \sqrt{b - 4 (a c)}}{2 a}$ $color(white)("XXX")x=(-color(blue)(b)+-sqrt(color(blue)(b)-4(color(red)(a)color(green)(c))))/(2color(red)(a))$

$x^{2} - 175 = 0$ $x^2-175=0$ is equivalent to
$XXX 1 x^{2} + 0 x + (- 175) = 0$ $color(white)("XXX")color(red)(1)x^2+color(blue)(0)x+color(green)(""(-175))=0$

So the solutions are
$XXX x = \frac{- 0 \pm \sqrt{0 - 4 \cdot (1 \cdot (- 175))}}{2 \cdot 1}$ $color(white)("XXX")x=(-color(blue)(0)+-sqrt(color(blue)(0)-4 * (color(red)(1) * color(green)(""(-175)))))/(2 * color(red)(1))$

$XXXX = \pm \frac{\sqrt{700}}{2}$ $color(white)("XXXX")=+-sqrt(700)/2$

$XXXX = \pm \frac{10 \sqrt{7}}{2}$ $color(white)("XXXX")=+-(10sqrt(7))/2$

$XXXX = \pm 5 \sqrt{7}$ $color(white)("XXXX")=+-5sqrt(7)$

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How do you solve $x^{2} - 175 = 0$ $x^2-175=0$ using the quadratic formula?

1 Answer

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How do you solve $x^{2} - 175 = 0$ $x^2-175=0$ using the quadratic formula?