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4x^{2}=31+45
Add 45 to both sides.
4x^{2}=76
Add 31 and 45 to get 76.
x^{2}=\frac{76}{4}
Divide both sides by 4.
x^{2}=19
Divide 76 by 4 to get 19.
x=\sqrt{19} x=-\sqrt{19}
Take the square root of both sides of the equation.
4x^{2}-45-31=0
Subtract 31 from both sides.
4x^{2}-76=0
Subtract 31 from -45 to get -76.
x=\frac{0±\sqrt{0^{2}-4\times 4\left(-76\right)}}{2\times 4}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -76 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 4\left(-76\right)}}{2\times 4}
Square 0.
x=\frac{0±\sqrt{-16\left(-76\right)}}{2\times 4}
Multiply -4 times 4.
x=\frac{0±\sqrt{1216}}{2\times 4}
Multiply -16 times -76.
x=\frac{0±8\sqrt{19}}{2\times 4}
Take the square root of 1216.
x=\frac{0±8\sqrt{19}}{8}
Multiply 2 times 4.
x=\sqrt{19}
Now solve the equation x=\frac{0±8\sqrt{19}}{8} when ± is plus.
x=-\sqrt{19}
Now solve the equation x=\frac{0±8\sqrt{19}}{8} when ± is minus.
x=\sqrt{19} x=-\sqrt{19}
The equation is now solved.