Solve 6^2-x^2=4^2-(6-x^2)

$$6 ^ { 2 } - x ^ { 2 } = 4 ^ { 2 } - ( 6 - x ^ { 2 } )$$

Solve for x

$$x=\sqrt{13}\approx 3.605551275$$

$$x=-\sqrt{13}\approx -3.605551275$$

Steps by Finding Square Root

Calculate 6 to the power of 2 and get 36.

$$36-x^{2}=4^{2}-\left(6-x^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$36-x^{2}=16-\left(6-x^{2}\right)$$

To find the opposite of 6-x^{2}, find the opposite of each term.

$$36-x^{2}=16-6+x^{2}$$

Subtract 6 from 16 to get 10.

$$36-x^{2}=10+x^{2}$$

Subtract x^{2} from both sides.

$$36-x^{2}-x^{2}=10$$

Combine -x^{2} and -x^{2} to get -2x^{2}.

$$36-2x^{2}=10$$

Subtract 36 from both sides.

$$-2x^{2}=10-36$$

Subtract 36 from 10 to get -26.

$$-2x^{2}=-26$$

Divide both sides by -2.

$$x^{2}=\frac{-26}{-2}$$

Divide -26 by -2 to get 13.

$$x^{2}=13$$

Take the square root of both sides of the equation.

$$x=\sqrt{13} x=-\sqrt{13}$$

Steps Using the Quadratic Formula

Calculate 6 to the power of 2 and get 36.

$$36-x^{2}=4^{2}-\left(6-x^{2}\right)$$

Calculate 4 to the power of 2 and get 16.

$$36-x^{2}=16-\left(6-x^{2}\right)$$

To find the opposite of 6-x^{2}, find the opposite of each term.

$$36-x^{2}=16-6+x^{2}$$

Subtract 6 from 16 to get 10.

$$36-x^{2}=10+x^{2}$$

Subtract 10 from both sides.

$$36-x^{2}-10=x^{2}$$

Subtract 10 from 36 to get 26.

$$26-x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$26-x^{2}-x^{2}=0$$

Combine -x^{2} and -x^{2} to get -2x^{2}.

$$26-2x^{2}=0$$

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.

$$-2x^{2}+26=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and 26 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 26}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 26}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\times 26}}{2\left(-2\right)}$$

Multiply 8 times 26.

$$x=\frac{0±\sqrt{208}}{2\left(-2\right)}$$

Take the square root of 208.

$$x=\frac{0±4\sqrt{13}}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±4\sqrt{13}}{-4}$$

Now solve the equation x=\frac{0±4\sqrt{13}}{-4} when ± is plus.

$$x=-\sqrt{13}$$

Now solve the equation x=\frac{0±4\sqrt{13}}{-4} when ± is minus.

$$x=\sqrt{13}$$

The equation is now solved.

$$x=-\sqrt{13} x=\sqrt{13}$$