Solve for x
x=\sqrt{6}\approx 2.449489743
x=-\sqrt{6}\approx -2.449489743
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5x^{2}=30
Add 30 to both sides. Anything plus zero gives itself.
x^{2}=\frac{30}{5}
Divide both sides by 5.
x^{2}=6
Divide 30 by 5 to get 6.
x=\sqrt{6} x=-\sqrt{6}
Take the square root of both sides of the equation.
5x^{2}-30=0
Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.
x=\frac{0±\sqrt{0^{2}-4\times 5\left(-30\right)}}{2\times 5}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -30 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 5\left(-30\right)}}{2\times 5}
Square 0.
x=\frac{0±\sqrt{-20\left(-30\right)}}{2\times 5}
Multiply -4 times 5.
x=\frac{0±\sqrt{600}}{2\times 5}
Multiply -20 times -30.
x=\frac{0±10\sqrt{6}}{2\times 5}
Take the square root of 600.
x=\frac{0±10\sqrt{6}}{10}
Multiply 2 times 5.
x=\sqrt{6}
Now solve the equation x=\frac{0±10\sqrt{6}}{10} when ± is plus.
x=-\sqrt{6}
Now solve the equation x=\frac{0±10\sqrt{6}}{10} when ± is minus.
x=\sqrt{6} x=-\sqrt{6}
The equation is now solved.
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