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1225+x^{2}=41^{2}
Calculate 35 to the power of 2 and get 1225.
1225+x^{2}=1681
Calculate 41 to the power of 2 and get 1681.
x^{2}=1681-1225
Subtract 1225 from both sides.
x^{2}=456
Subtract 1225 from 1681 to get 456.
x=2\sqrt{114} x=-2\sqrt{114}
Take the square root of both sides of the equation.
1225+x^{2}=41^{2}
Calculate 35 to the power of 2 and get 1225.
1225+x^{2}=1681
Calculate 41 to the power of 2 and get 1681.
1225+x^{2}-1681=0
Subtract 1681 from both sides.
-456+x^{2}=0
Subtract 1681 from 1225 to get -456.
x^{2}-456=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(-456\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -456 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\left(-456\right)}}{2}
Square 0.
x=\frac{0±\sqrt{1824}}{2}
Multiply -4 times -456.
x=\frac{0±4\sqrt{114}}{2}
Take the square root of 1824.
x=2\sqrt{114}
Now solve the equation x=\frac{0±4\sqrt{114}}{2} when ± is plus.
x=-2\sqrt{114}
Now solve the equation x=\frac{0±4\sqrt{114}}{2} when ± is minus.
x=2\sqrt{114} x=-2\sqrt{114}
The equation is now solved.