Solve 200^2-4(5+x^2)124=0

$${ 200 }^{ 2 } -4(5+ { x }^{ 2 } )124=0$$

Solve for x

$$x = \frac{\sqrt{72695}}{31} \approx 8.697422681$$

$$x = -\frac{\sqrt{72695}}{31} \approx -8.697422681$$

Steps by Finding Square Root

Calculate 200 to the power of 2 and get 40000.

$$40000-4\left(5+x^{2}\right)\times 124=0$$

Multiply 4 and 124 to get 496.

$$40000-496\left(5+x^{2}\right)=0$$

Use the distributive property to multiply -496 by 5+x^{2}.

$$40000-2480-496x^{2}=0$$

Subtract 2480 from 40000 to get 37520.

$$37520-496x^{2}=0$$

Subtract 37520 from both sides. Anything subtracted from zero gives its negation.

$$-496x^{2}=-37520$$

Divide both sides by -496.

$$x^{2}=\frac{-37520}{-496}$$

Reduce the fraction \frac{-37520}{-496} to lowest terms by extracting and canceling out -16.

$$x^{2}=\frac{2345}{31}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{72695}}{31} x=-\frac{\sqrt{72695}}{31}$$

Steps Using the Quadratic Formula

Calculate 200 to the power of 2 and get 40000.

$$40000-4\left(5+x^{2}\right)\times 124=0$$

Multiply 4 and 124 to get 496.

$$40000-496\left(5+x^{2}\right)=0$$

Use the distributive property to multiply -496 by 5+x^{2}.

$$40000-2480-496x^{2}=0$$

Subtract 2480 from 40000 to get 37520.

$$37520-496x^{2}=0$$

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.

$$-496x^{2}+37520=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -496 for a, 0 for b, and 37520 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-496\right)\times 37520}}{2\left(-496\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-496\right)\times 37520}}{2\left(-496\right)}$$

Multiply -4 times -496.

$$x=\frac{0±\sqrt{1984\times 37520}}{2\left(-496\right)}$$

Multiply 1984 times 37520.

$$x=\frac{0±\sqrt{74439680}}{2\left(-496\right)}$$

Take the square root of 74439680.

$$x=\frac{0±32\sqrt{72695}}{2\left(-496\right)}$$

Multiply 2 times -496.

$$x=\frac{0±32\sqrt{72695}}{-992}$$

Now solve the equation x=\frac{0±32\sqrt{72695}}{-992} when ± is plus.

$$x=-\frac{\sqrt{72695}}{31}$$

Now solve the equation x=\frac{0±32\sqrt{72695}}{-992} when ± is minus.

$$x=\frac{\sqrt{72695}}{31}$$

The equation is now solved.

$$x=-\frac{\sqrt{72695}}{31} x=\frac{\sqrt{72695}}{31}$$