Solve x^2=sqrt{6.25}

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

Solve for x

$$x = \frac{\sqrt{10}}{2} \approx 1.58113883$$

$$x = -\frac{\sqrt{10}}{2} \approx -1.58113883$$

Steps by Finding Square Root

Calculate the square root of 6.25 and get 2.5.

$$x^{2}=2.5$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{10}}{2} x=-\frac{\sqrt{10}}{2}$$

Steps Using the Quadratic Formula

Calculate the square root of 6.25 and get 2.5.

$$x^{2}=2.5$$

Subtract 2.5 from both sides.

$$x^{2}-2.5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2.5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2.5\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2.5\right)}}{2}$$

Multiply -4 times -2.5.

$$x=\frac{0±\sqrt{10}}{2}$$

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

$$x=\frac{\sqrt{10}}{2}$$

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

$$x=-\frac{\sqrt{10}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{10}}{2} x=-\frac{\sqrt{10}}{2}$$