Solve 110^2=2a^2

$$110 ^ { 2 } = 2 a ^ { 2 }$$

Solve for a

$$a=55\sqrt{2}\approx 77.781745931$$

$$a=-55\sqrt{2}\approx -77.781745931$$

Steps by Finding Square Root

Calculate 110 to the power of 2 and get 12100.

$$12100=2a^{2}$$

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

$$2a^{2}=12100$$

Divide both sides by 2.

$$a^{2}=\frac{12100}{2}$$

Divide 12100 by 2 to get 6050.

$$a^{2}=6050$$

Take the square root of both sides of the equation.

$$a=55\sqrt{2} a=-55\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 110 to the power of 2 and get 12100.

$$12100=2a^{2}$$

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

$$2a^{2}=12100$$

Subtract 12100 from both sides.

$$2a^{2}-12100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -12100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 2\left(-12100\right)}}{2\times 2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 2\left(-12100\right)}}{2\times 2}$$

Multiply -4 times 2.

$$a=\frac{0±\sqrt{-8\left(-12100\right)}}{2\times 2}$$

Multiply -8 times -12100.

$$a=\frac{0±\sqrt{96800}}{2\times 2}$$

Take the square root of 96800.

$$a=\frac{0±220\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$a=\frac{0±220\sqrt{2}}{4}$$

Now solve the equation a=\frac{0±220\sqrt{2}}{4} when ± is plus.

$$a=55\sqrt{2}$$

Now solve the equation a=\frac{0±220\sqrt{2}}{4} when ± is minus.

$$a=-55\sqrt{2}$$

The equation is now solved.

$$a=55\sqrt{2} a=-55\sqrt{2}$$