Solve a^2/36+frac{{left(sqrt{155+3}right)}^2}{9}=1

$$\frac{ { a }^{ 2 } }{ 36 } + \frac{ { \left( \sqrt{ 155+3 } \right) }^{ 2 } }{ 9 } = 1$$

Solve for a

$$a=-2\sqrt{149}i\approx -0-24.413111231i$$

$$a=2\sqrt{149}i\approx 24.413111231i$$

Steps by Finding Square Root

Multiply both sides of the equation by 36, the least common multiple of 36,9.

$$a^{2}+4\left(\sqrt{155+3}\right)^{2}=36$$

Add 155 and 3 to get 158.

$$a^{2}+4\left(\sqrt{158}\right)^{2}=36$$

The square of \sqrt{158} is 158.

$$a^{2}+4\times 158=36$$

Multiply 4 and 158 to get 632.

$$a^{2}+632=36$$

Subtract 632 from both sides.

$$a^{2}=36-632$$

Subtract 632 from 36 to get -596.

$$a^{2}=-596$$

The equation is now solved.

$$a=2\sqrt{149}i a=-2\sqrt{149}i$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 36, the least common multiple of 36,9.

$$a^{2}+4\left(\sqrt{155+3}\right)^{2}=36$$

Add 155 and 3 to get 158.

$$a^{2}+4\left(\sqrt{158}\right)^{2}=36$$

The square of \sqrt{158} is 158.

$$a^{2}+4\times 158=36$$

Multiply 4 and 158 to get 632.

$$a^{2}+632=36$$

Subtract 36 from both sides.

$$a^{2}+632-36=0$$

Subtract 36 from 632 to get 596.

$$a^{2}+596=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 596 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 596}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 596}}{2}$$

Multiply -4 times 596.

$$a=\frac{0±\sqrt{-2384}}{2}$$

Take the square root of -2384.

$$a=\frac{0±4\sqrt{149}i}{2}$$

Now solve the equation a=\frac{0±4\sqrt{149}i}{2} when ± is plus.

$$a=2\sqrt{149}i$$

Now solve the equation a=\frac{0±4\sqrt{149}i}{2} when ± is minus.

$$a=-2\sqrt{149}i$$

The equation is now solved.

$$a=2\sqrt{149}i a=-2\sqrt{149}i$$