Solve a^2+2i^2=29^2

$$a ^ { 2 } + 2 i ^ { 2 } = 29 ^ { 2 }$$

Solve for a

$$a=-\sqrt{843}\approx -29.034462282$$

$$a=\sqrt{843}\approx 29.034462282$$

Steps by Finding Square Root

Calculate i to the power of 2 and get -1.

$$a^{2}+2\left(-1\right)=29^{2}$$

Multiply 2 and -1 to get -2.

$$a^{2}-2=29^{2}$$

Calculate 29 to the power of 2 and get 841.

$$a^{2}-2=841$$

Add 2 to both sides.

$$a^{2}=841+2$$

Add 841 and 2 to get 843.

$$a^{2}=843$$

The equation is now solved.

$$a=\sqrt{843} a=-\sqrt{843}$$

Steps Using the Quadratic Formula

Calculate i to the power of 2 and get -1.

$$a^{2}+2\left(-1\right)=29^{2}$$

Multiply 2 and -1 to get -2.

$$a^{2}-2=29^{2}$$

Calculate 29 to the power of 2 and get 841.

$$a^{2}-2=841$$

Subtract 841 from both sides.

$$a^{2}-2-841=0$$

Subtract 841 from -2 to get -843.

$$a^{2}-843=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -843 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-843\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-843\right)}}{2}$$

Multiply -4 times -843.

$$a=\frac{0±\sqrt{3372}}{2}$$

Take the square root of 3372.

$$a=\frac{0±2\sqrt{843}}{2}$$

Now solve the equation a=\frac{0±2\sqrt{843}}{2} when ± is plus.

$$a=\sqrt{843}$$

Now solve the equation a=\frac{0±2\sqrt{843}}{2} when ± is minus.

$$a=-\sqrt{843}$$

The equation is now solved.

$$a=\sqrt{843} a=-\sqrt{843}$$