Solve 4078379=40400-a^2

$$4078379 = 40400 - a ^ { 2 }$$

Solve for a

$$a=-\sqrt{4037979}i\approx -0-2009.472318794i$$

$$a=\sqrt{4037979}i\approx 2009.472318794i$$

Steps by Finding Square Root

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

$$40400-a^{2}=4078379$$

Subtract 40400 from both sides.

$$-a^{2}=4078379-40400$$

Subtract 40400 from 4078379 to get 4037979.

$$-a^{2}=4037979$$

Divide both sides by -1.

$$a^{2}=-4037979$$

The equation is now solved.

$$a=\sqrt{4037979}i a=-\sqrt{4037979}i$$

Steps Using the Quadratic Formula

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

$$40400-a^{2}=4078379$$

Subtract 4078379 from both sides.

$$40400-a^{2}-4078379=0$$

Subtract 4078379 from 40400 to get -4037979.

$$-4037979-a^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-a^{2}-4037979=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -4037979 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-4037979\right)}}{2\left(-1\right)}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-1\right)\left(-4037979\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$a=\frac{0±\sqrt{4\left(-4037979\right)}}{2\left(-1\right)}$$

Multiply 4 times -4037979.

$$a=\frac{0±\sqrt{-16151916}}{2\left(-1\right)}$$

Take the square root of -16151916.

$$a=\frac{0±2\sqrt{4037979}i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$a=\frac{0±2\sqrt{4037979}i}{-2}$$

Now solve the equation a=\frac{0±2\sqrt{4037979}i}{-2} when ± is plus.

$$a=-\sqrt{4037979}i$$

Now solve the equation a=\frac{0±2\sqrt{4037979}i}{-2} when ± is minus.

$$a=\sqrt{4037979}i$$

The equation is now solved.

$$a=-\sqrt{4037979}i a=\sqrt{4037979}i$$