Solve 4000^2+x^2=4000.01^2

$$4000 ^ { 2 } + x ^ { 2 } = 4000.01 ^ { 2 }$$

Solve for x

$$x = \frac{3 \sqrt{88889}}{100} \approx 8.9442775$$

$$x = -\frac{3 \sqrt{88889}}{100} \approx -8.9442775$$

Steps by Finding Square Root

Calculate 4000 to the power of 2 and get 16000000.

$$16000000+x^{2}=4000.01^{2}$$

Calculate 4000.01 to the power of 2 and get 16000080.0001.

$$16000000+x^{2}=16000080.0001$$

Subtract 16000000 from both sides.

$$x^{2}=16000080.0001-16000000$$

Subtract 16000000 from 16000080.0001 to get 80.0001.

$$x^{2}=80.0001$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{88889}}{100} x=-\frac{3\sqrt{88889}}{100}$$

Steps Using the Quadratic Formula

Calculate 4000 to the power of 2 and get 16000000.

$$16000000+x^{2}=4000.01^{2}$$

Calculate 4000.01 to the power of 2 and get 16000080.0001.

$$16000000+x^{2}=16000080.0001$$

Subtract 16000080.0001 from both sides.

$$16000000+x^{2}-16000080.0001=0$$

Subtract 16000080.0001 from 16000000 to get -80.0001.

$$-80.0001+x^{2}=0$$

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.

$$x^{2}-80.0001=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -80.0001 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-80.0001\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-80.0001\right)}}{2}$$

Multiply -4 times -80.0001.

$$x=\frac{0±\sqrt{320.0004}}{2}$$

Take the square root of 320.0004.

$$x=\frac{0±\frac{3\sqrt{88889}}{50}}{2}$$

Now solve the equation x=\frac{0±\frac{3\sqrt{88889}}{50}}{2} when ± is plus.

$$x=\frac{3\sqrt{88889}}{100}$$

Now solve the equation x=\frac{0±\frac{3\sqrt{88889}}{50}}{2} when ± is minus.

$$x=-\frac{3\sqrt{88889}}{100}$$

The equation is now solved.

$$x=\frac{3\sqrt{88889}}{100} x=-\frac{3\sqrt{88889}}{100}$$