Solve 2x^2=2.5^2

$$2 { x }^{ 2 } = { 2.5 }^{ 2 }$$

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

Calculate 2.5 to the power of 2 and get 6.25.

$$2x^{2}=6.25$$

Divide both sides by 2.

$$x^{2}=\frac{6.25}{2}$$

Expand \frac{6.25}{2} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{625}{200}$$

Reduce the fraction \frac{625}{200} to lowest terms by extracting and canceling out 25.

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

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

Calculate 2.5 to the power of 2 and get 6.25.

$$2x^{2}=6.25$$

Subtract 6.25 from both sides.

$$2x^{2}-6.25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -6.25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-6.25\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-6.25\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-6.25\right)}}{2\times 2}$$

Multiply -8 times -6.25.

$$x=\frac{0±\sqrt{50}}{2\times 2}$$

Take the square root of 50.

$$x=\frac{0±5\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±5\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±5\sqrt{2}}{4} when ± is plus.

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

Now solve the equation x=\frac{0±5\sqrt{2}}{4} when ± is minus.

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

The equation is now solved.

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