Solve 13^2-(132)^3=10^2-x^2

$$13 ^ { 2 } - ( 132 ) ^ { 3 } = 10 ^ { 2 } - x ^ { 2 }$$

Solve for x

$$x=\sqrt{2299899}\approx 1516.541789731$$

$$x=-\sqrt{2299899}\approx -1516.541789731$$

Steps by Finding Square Root

Calculate 13 to the power of 2 and get 169.

$$169-132^{3}=10^{2}-x^{2}$$

Calculate 132 to the power of 3 and get 2299968.

$$169-2299968=10^{2}-x^{2}$$

Subtract 2299968 from 169 to get -2299799.

$$-2299799=10^{2}-x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$-2299799=100-x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$100-x^{2}=-2299799$$

Subtract 100 from both sides.

$$-x^{2}=-2299799-100$$

Subtract 100 from -2299799 to get -2299899.

$$-x^{2}=-2299899$$

Divide both sides by -1.

$$x^{2}=\frac{-2299899}{-1}$$

Fraction \frac{-2299899}{-1} can be simplified to 2299899 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=2299899$$

Take the square root of both sides of the equation.

$$x=\sqrt{2299899} x=-\sqrt{2299899}$$

Steps Using the Quadratic Formula

Calculate 13 to the power of 2 and get 169.

$$169-132^{3}=10^{2}-x^{2}$$

Calculate 132 to the power of 3 and get 2299968.

$$169-2299968=10^{2}-x^{2}$$

Subtract 2299968 from 169 to get -2299799.

$$-2299799=10^{2}-x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$-2299799=100-x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$100-x^{2}=-2299799$$

Add 2299799 to both sides.

$$100-x^{2}+2299799=0$$

Add 100 and 2299799 to get 2299899.

$$2299899-x^{2}=0$$

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.

$$-x^{2}+2299899=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 2299899 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 2299899}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 2299899}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 2299899}}{2\left(-1\right)}$$

Multiply 4 times 2299899.

$$x=\frac{0±\sqrt{9199596}}{2\left(-1\right)}$$

Take the square root of 9199596.

$$x=\frac{0±2\sqrt{2299899}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{2299899}}{-2}$$

Now solve the equation x=\frac{0±2\sqrt{2299899}}{-2} when ± is plus.

$$x=-\sqrt{2299899}$$

Now solve the equation x=\frac{0±2\sqrt{2299899}}{-2} when ± is minus.

$$x=\sqrt{2299899}$$

The equation is now solved.

$$x=-\sqrt{2299899} x=\sqrt{2299899}$$