Solve (102)^2=289a^2

$$( 102 ) ^ { 2 } = 289 a ^ { 2 }$$

Solve for a

$$a=6$$

$$a=-6$$

Steps Using Difference of Squares

Calculate 102 to the power of 2 and get 10404.

$$10404=289a^{2}$$

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

$$289a^{2}=10404$$

Subtract 10404 from both sides.

$$289a^{2}-10404=0$$

Divide both sides by 289.

$$a^{2}-36=0$$

Consider a^{2}-36. Rewrite a^{2}-36 as a^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(a-6\right)\left(a+6\right)=0$$

To find equation solutions, solve a-6=0 and a+6=0.

$$a=6 a=-6$$

Steps by Finding Square Root

Calculate 102 to the power of 2 and get 10404.

$$10404=289a^{2}$$

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

$$289a^{2}=10404$$

Divide both sides by 289.

$$a^{2}=\frac{10404}{289}$$

Divide 10404 by 289 to get 36.

$$a^{2}=36$$

Take the square root of both sides of the equation.

$$a=6 a=-6$$

Steps Using the Quadratic Formula

Calculate 102 to the power of 2 and get 10404.

$$10404=289a^{2}$$

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

$$289a^{2}=10404$$

Subtract 10404 from both sides.

$$289a^{2}-10404=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 289 for a, 0 for b, and -10404 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 289\left(-10404\right)}}{2\times 289}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 289\left(-10404\right)}}{2\times 289}$$

Multiply -4 times 289.

$$a=\frac{0±\sqrt{-1156\left(-10404\right)}}{2\times 289}$$

Multiply -1156 times -10404.

$$a=\frac{0±\sqrt{12027024}}{2\times 289}$$

Take the square root of 12027024.

$$a=\frac{0±3468}{2\times 289}$$

Multiply 2 times 289.

$$a=\frac{0±3468}{578}$$

Now solve the equation a=\frac{0±3468}{578} when ± is plus. Divide 3468 by 578.

$$a=6$$

Now solve the equation a=\frac{0±3468}{578} when ± is minus. Divide -3468 by 578.

$$a=-6$$

The equation is now solved.

$$a=6 a=-6$$