Solve [400-10(x-8)]x=4950

$$[ 400 - 10 ( x - 8 ) ] x = 4950$$

Solve for x

$$x=15$$

$$x=33$$

Steps Using the Quadratic Formula

Use the distributive property to multiply -10 by x-8.

$$\left(400-10x+80\right)x=4950$$

Add 400 and 80 to get 480.

$$\left(480-10x\right)x=4950$$

Use the distributive property to multiply 480-10x by x.

$$480x-10x^{2}=4950$$

Subtract 4950 from both sides.

$$480x-10x^{2}-4950=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-10x^{2}+480x-4950=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -10 for a, 480 for b, and -4950 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-480±\sqrt{480^{2}-4\left(-10\right)\left(-4950\right)}}{2\left(-10\right)}$$

Square 480.

$$x=\frac{-480±\sqrt{230400-4\left(-10\right)\left(-4950\right)}}{2\left(-10\right)}$$

Multiply -4 times -10.

$$x=\frac{-480±\sqrt{230400+40\left(-4950\right)}}{2\left(-10\right)}$$

Multiply 40 times -4950.

$$x=\frac{-480±\sqrt{230400-198000}}{2\left(-10\right)}$$

Add 230400 to -198000.

$$x=\frac{-480±\sqrt{32400}}{2\left(-10\right)}$$

Take the square root of 32400.

$$x=\frac{-480±180}{2\left(-10\right)}$$

Multiply 2 times -10.

$$x=\frac{-480±180}{-20}$$

Now solve the equation x=\frac{-480±180}{-20} when ± is plus. Add -480 to 180.

$$x=-\frac{300}{-20}$$

Divide -300 by -20.

$$x=15$$

Now solve the equation x=\frac{-480±180}{-20} when ± is minus. Subtract 180 from -480.

$$x=-\frac{660}{-20}$$

Divide -660 by -20.

$$x=33$$

The equation is now solved.

$$x=15 x=33$$

Steps for Completing the Square

Use the distributive property to multiply -10 by x-8.

$$\left(400-10x+80\right)x=4950$$

Add 400 and 80 to get 480.

$$\left(480-10x\right)x=4950$$

Use the distributive property to multiply 480-10x by x.

$$480x-10x^{2}=4950$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-10x^{2}+480x=4950$$

Divide both sides by -10.

$$\frac{-10x^{2}+480x}{-10}=\frac{4950}{-10}$$

Dividing by -10 undoes the multiplication by -10.

$$x^{2}+\frac{480}{-10}x=\frac{4950}{-10}$$

Divide 480 by -10.

$$x^{2}-48x=\frac{4950}{-10}$$

Divide 4950 by -10.

$$x^{2}-48x=-495$$

Divide -48, the coefficient of the x term, by 2 to get -24. Then add the square of -24 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-48x+\left(-24\right)^{2}=-495+\left(-24\right)^{2}$$

Square -24.

$$x^{2}-48x+576=-495+576$$

Add -495 to 576.

$$x^{2}-48x+576=81$$

Factor x^{2}-48x+576. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-24\right)^{2}=81$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-24\right)^{2}}=\sqrt{81}$$

Simplify.

$$x-24=9 x-24=-9$$

Add 24 to both sides of the equation.

$$x=33 x=15$$