Solve 4000^2+x^2=(4000+12500)^2

$$4000 ^ { 2 } + x ^ { 2 } = ( 4000 + 12500 ) ^ { 2 }$$

Solve for x

$$x=2500\sqrt{41}\approx 16007.810593582$$

$$x=-2500\sqrt{41}\approx -16007.810593582$$

Steps by Finding Square Root

Calculate 4000 to the power of 2 and get 16000000.

$$16000000+x^{2}=\left(4000+12500\right)^{2}$$

Add 4000 and 12500 to get 16500.

$$16000000+x^{2}=16500^{2}$$

Calculate 16500 to the power of 2 and get 272250000.

$$16000000+x^{2}=272250000$$

Subtract 16000000 from both sides.

$$x^{2}=272250000-16000000$$

Subtract 16000000 from 272250000 to get 256250000.

$$x^{2}=256250000$$

Take the square root of both sides of the equation.

$$x=2500\sqrt{41} x=-2500\sqrt{41}$$

Steps Using the Quadratic Formula

Calculate 4000 to the power of 2 and get 16000000.

$$16000000+x^{2}=\left(4000+12500\right)^{2}$$

Add 4000 and 12500 to get 16500.

$$16000000+x^{2}=16500^{2}$$

Calculate 16500 to the power of 2 and get 272250000.

$$16000000+x^{2}=272250000$$

Subtract 272250000 from both sides.

$$16000000+x^{2}-272250000=0$$

Subtract 272250000 from 16000000 to get -256250000.

$$-256250000+x^{2}=0$$

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.

$$x^{2}-256250000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -256250000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-256250000\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-256250000\right)}}{2}$$

Multiply -4 times -256250000.

$$x=\frac{0±\sqrt{1025000000}}{2}$$

Take the square root of 1025000000.

$$x=\frac{0±5000\sqrt{41}}{2}$$

Now solve the equation x=\frac{0±5000\sqrt{41}}{2} when ± is plus.

$$x=2500\sqrt{41}$$

Now solve the equation x=\frac{0±5000\sqrt{41}}{2} when ± is minus.

$$x=-2500\sqrt{41}$$

The equation is now solved.

$$x=2500\sqrt{41} x=-2500\sqrt{41}$$