Solve 6400=(240-4x)(60+x)

$$6400 = ( 240 - 4 x ) ( 60 + x )$$

Solve for x

$$x=20\sqrt{5}\approx 44.72135955$$

$$x=-20\sqrt{5}\approx -44.72135955$$

Steps by Finding Square Root

Use the distributive property to multiply 240-4x by 60+x and combine like terms.

$$6400=14400-4x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$14400-4x^{2}=6400$$

Subtract 14400 from both sides.

$$-4x^{2}=6400-14400$$

Subtract 14400 from 6400 to get -8000.

$$-4x^{2}=-8000$$

Divide both sides by -4.

$$x^{2}=\frac{-8000}{-4}$$

Divide -8000 by -4 to get 2000.

$$x^{2}=2000$$

Take the square root of both sides of the equation.

$$x=20\sqrt{5} x=-20\sqrt{5}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 240-4x by 60+x and combine like terms.

$$6400=14400-4x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$14400-4x^{2}=6400$$

Subtract 6400 from both sides.

$$14400-4x^{2}-6400=0$$

Subtract 6400 from 14400 to get 8000.

$$8000-4x^{2}=0$$

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.

$$-4x^{2}+8000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and 8000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 8000}}{2\left(-4\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4\right)\times 8000}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$x=\frac{0±\sqrt{16\times 8000}}{2\left(-4\right)}$$

Multiply 16 times 8000.

$$x=\frac{0±\sqrt{128000}}{2\left(-4\right)}$$

Take the square root of 128000.

$$x=\frac{0±160\sqrt{5}}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±160\sqrt{5}}{-8}$$

Now solve the equation x=\frac{0±160\sqrt{5}}{-8} when ± is plus.

$$x=-20\sqrt{5}$$

Now solve the equation x=\frac{0±160\sqrt{5}}{-8} when ± is minus.

$$x=20\sqrt{5}$$

The equation is now solved.

$$x=-20\sqrt{5} x=20\sqrt{5}$$