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98.01+x^{2}=12.5^{2}
Calculate 9.9 to the power of 2 and get 98.01.
98.01+x^{2}=156.25
Calculate 12.5 to the power of 2 and get 156.25.
x^{2}=156.25-98.01
Subtract 98.01 from both sides.
x^{2}=58.24
Subtract 98.01 from 156.25 to get 58.24.
x=\frac{4\sqrt{91}}{5} x=-\frac{4\sqrt{91}}{5}
Take the square root of both sides of the equation.
98.01+x^{2}=12.5^{2}
Calculate 9.9 to the power of 2 and get 98.01.
98.01+x^{2}=156.25
Calculate 12.5 to the power of 2 and get 156.25.
98.01+x^{2}-156.25=0
Subtract 156.25 from both sides.
-58.24+x^{2}=0
Subtract 156.25 from 98.01 to get -58.24.
x^{2}-58.24=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(-58.24\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -58.24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-58.24\right)}}{2}
Square 0.
x=\frac{0±\sqrt{232.96}}{2}
Multiply -4 times -58.24.
x=\frac{0±\frac{8\sqrt{91}}{5}}{2}
Take the square root of 232.96.
x=\frac{4\sqrt{91}}{5}
Now solve the equation x=\frac{0±\frac{8\sqrt{91}}{5}}{2} when ± is plus.
x=-\frac{4\sqrt{91}}{5}
Now solve the equation x=\frac{0±\frac{8\sqrt{91}}{5}}{2} when ± is minus.
x=\frac{4\sqrt{91}}{5} x=-\frac{4\sqrt{91}}{5}
The equation is now solved.