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3x^{2}=63
Add 63 to both sides. Anything plus zero gives itself.
x^{2}=\frac{63}{3}
Divide both sides by 3.
x^{2}=21
Divide 63 by 3 to get 21.
x=\sqrt{21} x=-\sqrt{21}
Take the square root of both sides of the equation.
3x^{2}-63=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 3\left(-63\right)}}{2\times 3}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -63 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 3\left(-63\right)}}{2\times 3}
Square 0.
x=\frac{0±\sqrt{-12\left(-63\right)}}{2\times 3}
Multiply -4 times 3.
x=\frac{0±\sqrt{756}}{2\times 3}
Multiply -12 times -63.
x=\frac{0±6\sqrt{21}}{2\times 3}
Take the square root of 756.
x=\frac{0±6\sqrt{21}}{6}
Multiply 2 times 3.
x=\sqrt{21}
Now solve the equation x=\frac{0±6\sqrt{21}}{6} when ± is plus.
x=-\sqrt{21}
Now solve the equation x=\frac{0±6\sqrt{21}}{6} when ± is minus.
x=\sqrt{21} x=-\sqrt{21}
The equation is now solved.