Solve 25.7=3.14x^2

$$25.7=3.14 { x }^{ 2 }$$

Solve for x

$$x = \frac{\sqrt{201745}}{157} \approx 2.860893807$$

$$x = -\frac{\sqrt{201745}}{157} \approx -2.860893807$$

Steps by Finding Square Root

Divide both sides by 3.14.

$$\frac{25.7}{3.14}=x^{2}$$

Expand \frac{25.7}{3.14} by multiplying both numerator and the denominator by 100.

$$\frac{2570}{314}=x^{2}$$

Reduce the fraction \frac{2570}{314} to lowest terms by extracting and canceling out 2.

$$\frac{1285}{157}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{1285}{157}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{201745}}{157} x=-\frac{\sqrt{201745}}{157}$$

Steps Using the Quadratic Formula

Divide both sides by 3.14.

$$\frac{25.7}{3.14}=x^{2}$$

Expand \frac{25.7}{3.14} by multiplying both numerator and the denominator by 100.

$$\frac{2570}{314}=x^{2}$$

Reduce the fraction \frac{2570}{314} to lowest terms by extracting and canceling out 2.

$$\frac{1285}{157}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{1285}{157}$$

Subtract \frac{1285}{157} from both sides.

$$x^{2}-\frac{1285}{157}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1285}{157} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1285}{157}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1285}{157}\right)}}{2}$$

Multiply -4 times -\frac{1285}{157}.

$$x=\frac{0±\sqrt{\frac{5140}{157}}}{2}$$

Take the square root of \frac{5140}{157}.

$$x=\frac{0±\frac{2\sqrt{201745}}{157}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{201745}}{157}}{2} when ± is plus.

$$x=\frac{\sqrt{201745}}{157}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{201745}}{157}}{2} when ± is minus.

$$x=-\frac{\sqrt{201745}}{157}$$

The equation is now solved.

$$x=\frac{\sqrt{201745}}{157} x=-\frac{\sqrt{201745}}{157}$$