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9801+x^{2}=125^{2}
Calculate 99 to the power of 2 and get 9801.
9801+x^{2}=15625
Calculate 125 to the power of 2 and get 15625.
x^{2}=15625-9801
Subtract 9801 from both sides.
x^{2}=5824
Subtract 9801 from 15625 to get 5824.
x=8\sqrt{91} x=-8\sqrt{91}
Take the square root of both sides of the equation.
9801+x^{2}=125^{2}
Calculate 99 to the power of 2 and get 9801.
9801+x^{2}=15625
Calculate 125 to the power of 2 and get 15625.
9801+x^{2}-15625=0
Subtract 15625 from both sides.
-5824+x^{2}=0
Subtract 15625 from 9801 to get -5824.
x^{2}-5824=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\left(-5824\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -5824 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-5824\right)}}{2}
Square 0.
x=\frac{0±\sqrt{23296}}{2}
Multiply -4 times -5824.
x=\frac{0±16\sqrt{91}}{2}
Take the square root of 23296.
x=8\sqrt{91}
Now solve the equation x=\frac{0±16\sqrt{91}}{2} when ± is plus.
x=-8\sqrt{91}
Now solve the equation x=\frac{0±16\sqrt{91}}{2} when ± is minus.
x=8\sqrt{91} x=-8\sqrt{91}
The equation is now solved.