Solve 5x^2=256-x^2

$$5 x ^ { 2 } = 256 - x ^ { 2 }$$

Solve for x

$$x = \frac{8 \sqrt{6}}{3} \approx 6.531972647$$

$$x = -\frac{8 \sqrt{6}}{3} \approx -6.531972647$$

Steps by Finding Square Root

Add x^{2} to both sides.

$$5x^{2}+x^{2}=256$$

Combine 5x^{2} and x^{2} to get 6x^{2}.

$$6x^{2}=256$$

Divide both sides by 6.

$$x^{2}=\frac{256}{6}$$

Reduce the fraction \frac{256}{6} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{128}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{8\sqrt{6}}{3} x=-\frac{8\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Subtract 256 from both sides.

$$5x^{2}-256=-x^{2}$$

Add x^{2} to both sides.

$$5x^{2}-256+x^{2}=0$$

Combine 5x^{2} and x^{2} to get 6x^{2}.

$$6x^{2}-256=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -256 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-256\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-256\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-256\right)}}{2\times 6}$$

Multiply -24 times -256.

$$x=\frac{0±\sqrt{6144}}{2\times 6}$$

Take the square root of 6144.

$$x=\frac{0±32\sqrt{6}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±32\sqrt{6}}{12}$$

Now solve the equation x=\frac{0±32\sqrt{6}}{12} when ± is plus.

$$x=\frac{8\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±32\sqrt{6}}{12} when ± is minus.

$$x=-\frac{8\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{8\sqrt{6}}{3} x=-\frac{8\sqrt{6}}{3}$$