Solve x^2=31/8

$$x ^ { 2 } = 3 \frac { 1 } { 8 }$$

Solve for x

$$x = \frac{5 \sqrt{2}}{4} \approx 1.767766953$$

$$x = -\frac{5 \sqrt{2}}{4} \approx -1.767766953$$

Steps by Finding Square Root

Multiply both sides of the equation by 8.

$$8x^{2}=3\times 8+1$$

Multiply 3 and 8 to get 24.

$$8x^{2}=24+1$$

Add 24 and 1 to get 25.

$$8x^{2}=25$$

Divide both sides by 8.

$$x^{2}=\frac{25}{8}$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{2}}{4} x=-\frac{5\sqrt{2}}{4}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 8.

$$8x^{2}=3\times 8+1$$

Multiply 3 and 8 to get 24.

$$8x^{2}=24+1$$

Add 24 and 1 to get 25.

$$8x^{2}=25$$

Subtract 25 from both sides.

$$8x^{2}-25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-25\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-25\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-25\right)}}{2\times 8}$$

Multiply -32 times -25.

$$x=\frac{0±\sqrt{800}}{2\times 8}$$

Take the square root of 800.

$$x=\frac{0±20\sqrt{2}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±20\sqrt{2}}{16}$$

Now solve the equation x=\frac{0±20\sqrt{2}}{16} when ± is plus.

$$x=\frac{5\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±20\sqrt{2}}{16} when ± is minus.

$$x=-\frac{5\sqrt{2}}{4}$$

The equation is now solved.

$$x=\frac{5\sqrt{2}}{4} x=-\frac{5\sqrt{2}}{4}$$