How do you solve $x^{2} - 30 = 0$ $x^2-30=0$ using the quadratic formula?

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Answer 1 · 2016-06-16T02:23:30

The quadratic formula requires us to put our quadratic into standard form:

$a x^{2} + b x + c = 0$ $ax^2+bx+c=0$

Our quadratic is already in this form:

$x^{2} - 30 = 1 x^{2} + 0 x - 30 = 0$ $x^2-30= 1x^2 + 0x -30 =0$

Therefore

$a = 1, b = 0 & c = - 30$ $a=1," " b=0 " & " c=-30$

Then we use the quadratic formula:

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

$x_{\pm} = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot (- 30)}}{2 \cdot 1}$ $x_(+-) = (0+-sqrt(0-4*1*(-30)))/(2*1)$

$x_{\pm} = \pm \frac{\sqrt{120}}{2}$ $x_(+-) = +-sqrt(120)/(2)$

we can bring the $2$ $2$ from the denominator up into the square root by first squaring it

$x_{\pm} = \pm \sqrt{\frac{120}{4}} = \pm \sqrt{30}$ $x_(+-) = +-sqrt(120/4)=+-sqrt(30)$

Which is the answer that we would have arrived at by just moving the $- 30$ $-30$ to the right hand side and taking the square root of both sides.

How do you solve x^2-30=0x2−30=0x^2-30=0 using the quadratic formula?