Solve 1000^2+p^2=100

$$1000 ^ { 2 } + p ^ { 2 } = 100$$

Solve for p

$$p=-30\sqrt{1111}i\approx -0-999.94999875i$$

$$p=30\sqrt{1111}i\approx 999.94999875i$$

Steps by Finding Square Root

Calculate 1000 to the power of 2 and get 1000000.

$$1000000+p^{2}=100$$

Subtract 1000000 from both sides.

$$p^{2}=100-1000000$$

Subtract 1000000 from 100 to get -999900.

$$p^{2}=-999900$$

The equation is now solved.

$$p=30\sqrt{1111}i p=-30\sqrt{1111}i$$

Steps Using the Quadratic Formula

Calculate 1000 to the power of 2 and get 1000000.

$$1000000+p^{2}=100$$

Subtract 100 from both sides.

$$1000000+p^{2}-100=0$$

Subtract 100 from 1000000 to get 999900.

$$999900+p^{2}=0$$

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.

$$p^{2}+999900=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 999900 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\times 999900}}{2}$$

Square 0.

$$p=\frac{0±\sqrt{-4\times 999900}}{2}$$

Multiply -4 times 999900.

$$p=\frac{0±\sqrt{-3999600}}{2}$$

Take the square root of -3999600.

$$p=\frac{0±60\sqrt{1111}i}{2}$$

Now solve the equation p=\frac{0±60\sqrt{1111}i}{2} when ± is plus.

$$p=30\sqrt{1111}i$$

Now solve the equation p=\frac{0±60\sqrt{1111}i}{2} when ± is minus.

$$p=-30\sqrt{1111}i$$

The equation is now solved.

$$p=30\sqrt{1111}i p=-30\sqrt{1111}i$$