Solve for x
x=\sqrt{94}\approx 9.695359715
x=-\sqrt{94}\approx -9.695359715
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2x^{2}=188
Add 188 to both sides. Anything plus zero gives itself.
x^{2}=\frac{188}{2}
Divide both sides by 2.
x^{2}=94
Divide 188 by 2 to get 94.
x=\sqrt{94} x=-\sqrt{94}
Take the square root of both sides of the equation.
2x^{2}-188=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 2\left(-188\right)}}{2\times 2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -188 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 2\left(-188\right)}}{2\times 2}
Square 0.
x=\frac{0±\sqrt{-8\left(-188\right)}}{2\times 2}
Multiply -4 times 2.
x=\frac{0±\sqrt{1504}}{2\times 2}
Multiply -8 times -188.
x=\frac{0±4\sqrt{94}}{2\times 2}
Take the square root of 1504.
x=\frac{0±4\sqrt{94}}{4}
Multiply 2 times 2.
x=\sqrt{94}
Now solve the equation x=\frac{0±4\sqrt{94}}{4} when ± is plus.
x=-\sqrt{94}
Now solve the equation x=\frac{0±4\sqrt{94}}{4} when ± is minus.
x=\sqrt{94} x=-\sqrt{94}
The equation is now solved.
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