Solve (2900-2500-50x)(8+x)=5000

$$(2900-2500-50x)(8+x)=5000$$

Solve for x (complex solution)

$$x=6i$$

$$x=-6i$$

Steps by Finding Square Root

Subtract 2500 from 2900 to get 400.

$$\left(400-50x\right)\left(8+x\right)=5000$$

Use the distributive property to multiply 400-50x by 8+x and combine like terms.

$$3200-50x^{2}=5000$$

Subtract 3200 from both sides.

$$-50x^{2}=5000-3200$$

Subtract 3200 from 5000 to get 1800.

$$-50x^{2}=1800$$

Divide both sides by -50.

$$x^{2}=\frac{1800}{-50}$$

Divide 1800 by -50 to get -36.

$$x^{2}=-36$$

The equation is now solved.

$$x=6i x=-6i$$

Steps Using the Quadratic Formula

Subtract 2500 from 2900 to get 400.

$$\left(400-50x\right)\left(8+x\right)=5000$$

Use the distributive property to multiply 400-50x by 8+x and combine like terms.

$$3200-50x^{2}=5000$$

Subtract 5000 from both sides.

$$3200-50x^{2}-5000=0$$

Subtract 5000 from 3200 to get -1800.

$$-1800-50x^{2}=0$$

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.

$$-50x^{2}-1800=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -50 for a, 0 for b, and -1800 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-50\right)\left(-1800\right)}}{2\left(-50\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-50\right)\left(-1800\right)}}{2\left(-50\right)}$$

Multiply -4 times -50.

$$x=\frac{0±\sqrt{200\left(-1800\right)}}{2\left(-50\right)}$$

Multiply 200 times -1800.

$$x=\frac{0±\sqrt{-360000}}{2\left(-50\right)}$$

Take the square root of -360000.

$$x=\frac{0±600i}{2\left(-50\right)}$$

Multiply 2 times -50.

$$x=\frac{0±600i}{-100}$$

Now solve the equation x=\frac{0±600i}{-100} when ± is plus.

$$x=-6i$$

Now solve the equation x=\frac{0±600i}{-100} when ± is minus.

$$x=6i$$

The equation is now solved.

$$x=-6i x=6i$$