Solve 22x^2=3.100^2

$$22 x ^ { 2 } = 3.100 ^ { 2 }$$

Solve for x

$$x=\frac{31\sqrt{22}}{220}\approx 0.660922221$$

$$x=-\frac{31\sqrt{22}}{220}\approx -0.660922221$$

Steps by Finding Square Root

Calculate 3.1 to the power of 2 and get 9.61.

$$22x^{2}=9.61$$

Divide both sides by 22.

$$x^{2}=\frac{9.61}{22}$$

Expand \frac{9.61}{22} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{961}{2200}$$

Take the square root of both sides of the equation.

$$x=\frac{31\sqrt{22}}{220} x=-\frac{31\sqrt{22}}{220}$$

Steps Using the Quadratic Formula

Calculate 3.1 to the power of 2 and get 9.61.

$$22x^{2}=9.61$$

Subtract 9.61 from both sides.

$$22x^{2}-9.61=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 22 for a, 0 for b, and -9.61 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 22\left(-9.61\right)}}{2\times 22}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 22\left(-9.61\right)}}{2\times 22}$$

Multiply -4 times 22.

$$x=\frac{0±\sqrt{-88\left(-9.61\right)}}{2\times 22}$$

Multiply -88 times -9.61.

$$x=\frac{0±\sqrt{845.68}}{2\times 22}$$

Take the square root of 845.68.

$$x=\frac{0±\frac{31\sqrt{22}}{5}}{2\times 22}$$

Multiply 2 times 22.

$$x=\frac{0±\frac{31\sqrt{22}}{5}}{44}$$

Now solve the equation x=\frac{0±\frac{31\sqrt{22}}{5}}{44} when ± is plus.

$$x=\frac{31\sqrt{22}}{220}$$

Now solve the equation x=\frac{0±\frac{31\sqrt{22}}{5}}{44} when ± is minus.

$$x=-\frac{31\sqrt{22}}{220}$$

The equation is now solved.

$$x=\frac{31\sqrt{22}}{220} x=-\frac{31\sqrt{22}}{220}$$