Solve a^2+(11)^2=(30)^2

$$a ^ { 2 } + ( 11 ) ^ { 2 } = ( 30 ) ^ { 2 }$$

Solve for a

$$a=\sqrt{779}\approx 27.910571474$$

$$a=-\sqrt{779}\approx -27.910571474$$

Steps by Finding Square Root

Calculate 11 to the power of 2 and get 121.

$$a^{2}+121=30^{2}$$

Calculate 30 to the power of 2 and get 900.

$$a^{2}+121=900$$

Subtract 121 from both sides.

$$a^{2}=900-121$$

Subtract 121 from 900 to get 779.

$$a^{2}=779$$

Take the square root of both sides of the equation.

$$a=\sqrt{779} a=-\sqrt{779}$$

Steps Using the Quadratic Formula

Calculate 11 to the power of 2 and get 121.

$$a^{2}+121=30^{2}$$

Calculate 30 to the power of 2 and get 900.

$$a^{2}+121=900$$

Subtract 900 from both sides.

$$a^{2}+121-900=0$$

Subtract 900 from 121 to get -779.

$$a^{2}-779=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -779 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-779\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-779\right)}}{2}$$

Multiply -4 times -779.

$$a=\frac{0±\sqrt{3116}}{2}$$

Take the square root of 3116.

$$a=\frac{0±2\sqrt{779}}{2}$$

Now solve the equation a=\frac{0±2\sqrt{779}}{2} when ± is plus.

$$a=\sqrt{779}$$

Now solve the equation a=\frac{0±2\sqrt{779}}{2} when ± is minus.

$$a=-\sqrt{779}$$

The equation is now solved.

$$a=\sqrt{779} a=-\sqrt{779}$$