Solve 77=3.14*x*x

$$77=3.14 \times x \times x$$

Solve for x

$$x = \frac{5 \sqrt{24178}}{157} \approx 4.951998889$$

$$x = -\frac{5 \sqrt{24178}}{157} \approx -4.951998889$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$77=3.14x^{2}$$

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

$$3.14x^{2}=77$$

Divide both sides by 3.14.

$$x^{2}=\frac{77}{3.14}$$

Expand \frac{77}{3.14} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{7700}{314}$$

Reduce the fraction \frac{7700}{314} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{3850}{157}$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{24178}}{157} x=-\frac{5\sqrt{24178}}{157}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$77=3.14x^{2}$$

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

$$3.14x^{2}=77$$

Subtract 77 from both sides.

$$3.14x^{2}-77=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3.14 for a, 0 for b, and -77 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3.14\left(-77\right)}}{2\times 3.14}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3.14\left(-77\right)}}{2\times 3.14}$$

Multiply -4 times 3.14.

$$x=\frac{0±\sqrt{-12.56\left(-77\right)}}{2\times 3.14}$$

Multiply -12.56 times -77.

$$x=\frac{0±\sqrt{967.12}}{2\times 3.14}$$

Take the square root of 967.12.

$$x=\frac{0±\frac{\sqrt{24178}}{5}}{2\times 3.14}$$

Multiply 2 times 3.14.

$$x=\frac{0±\frac{\sqrt{24178}}{5}}{6.28}$$

Now solve the equation x=\frac{0±\frac{\sqrt{24178}}{5}}{6.28} when ± is plus.

$$x=\frac{5\sqrt{24178}}{157}$$

Now solve the equation x=\frac{0±\frac{\sqrt{24178}}{5}}{6.28} when ± is minus.

$$x=-\frac{5\sqrt{24178}}{157}$$

The equation is now solved.

$$x=\frac{5\sqrt{24178}}{157} x=-\frac{5\sqrt{24178}}{157}$$