Solve 64-x^2=39

$$64- { x }^{ 2 } =39$$

Solve for x

$$x=5$$

$$x=-5$$

Steps by Finding Square Root

Subtract 64 from both sides.

$$-x^{2}=39-64$$

Subtract 64 from 39 to get -25.

$$-x^{2}=-25$$

Divide both sides by -1.

$$x^{2}=\frac{-25}{-1}$$

Fraction \frac{-25}{-1} can be simplified to 25 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=25$$

Take the square root of both sides of the equation.

$$x=5 x=-5$$

Steps Using the Quadratic Formula

Subtract 39 from both sides.

$$64-x^{2}-39=0$$

Subtract 39 from 64 to get 25.

$$25-x^{2}=0$$

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.

$$-x^{2}+25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 25}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 25}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 25}}{2\left(-1\right)}$$

Multiply 4 times 25.

$$x=\frac{0±\sqrt{100}}{2\left(-1\right)}$$

Take the square root of 100.

$$x=\frac{0±10}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±10}{-2}$$

Now solve the equation x=\frac{0±10}{-2} when ± is plus. Divide 10 by -2.

$$x=-5$$

Now solve the equation x=\frac{0±10}{-2} when ± is minus. Divide -10 by -2.

$$x=5$$

The equation is now solved.

$$x=-5 x=5$$