Solve left(92-2xright)left(60-xright)=6*885

$$\left( 92-2x \right) \left( 60-x \right) = 6 \cdot 885$$

Solve for x

$$x=1$$

$$x=105$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 92-2x by 60-x and combine like terms.

$$5520-212x+2x^{2}=6\times 885$$

Multiply 6 and 885 to get 5310.

$$5520-212x+2x^{2}=5310$$

Subtract 5310 from both sides.

$$5520-212x+2x^{2}-5310=0$$

Subtract 5310 from 5520 to get 210.

$$210-212x+2x^{2}=0$$

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.

$$2x^{2}-212x+210=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -212 for b, and 210 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-212\right)±\sqrt{\left(-212\right)^{2}-4\times 2\times 210}}{2\times 2}$$

Square -212.

$$x=\frac{-\left(-212\right)±\sqrt{44944-4\times 2\times 210}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-212\right)±\sqrt{44944-8\times 210}}{2\times 2}$$

Multiply -8 times 210.

$$x=\frac{-\left(-212\right)±\sqrt{44944-1680}}{2\times 2}$$

Add 44944 to -1680.

$$x=\frac{-\left(-212\right)±\sqrt{43264}}{2\times 2}$$

Take the square root of 43264.

$$x=\frac{-\left(-212\right)±208}{2\times 2}$$

The opposite of -212 is 212.

$$x=\frac{212±208}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{212±208}{4}$$

Now solve the equation x=\frac{212±208}{4} when ± is plus. Add 212 to 208.

$$x=\frac{420}{4}$$

Divide 420 by 4.

$$x=105$$

Now solve the equation x=\frac{212±208}{4} when ± is minus. Subtract 208 from 212.

$$x=\frac{4}{4}$$

Divide 4 by 4.

$$x=1$$

The equation is now solved.

$$x=105 x=1$$

Steps for Completing the Square

Use the distributive property to multiply 92-2x by 60-x and combine like terms.

$$5520-212x+2x^{2}=6\times 885$$

Multiply 6 and 885 to get 5310.

$$5520-212x+2x^{2}=5310$$

Subtract 5520 from both sides.

$$-212x+2x^{2}=5310-5520$$

Subtract 5520 from 5310 to get -210.

$$-212x+2x^{2}=-210$$

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.

$$2x^{2}-212x=-210$$

Divide both sides by 2.

$$\frac{2x^{2}-212x}{2}=-\frac{210}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\left(-\frac{212}{2}\right)x=-\frac{210}{2}$$

Divide -212 by 2.

$$x^{2}-106x=-\frac{210}{2}$$

Divide -210 by 2.

$$x^{2}-106x=-105$$

Divide -106, the coefficient of the x term, by 2 to get -53. Then add the square of -53 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-106x+\left(-53\right)^{2}=-105+\left(-53\right)^{2}$$

Square -53.

$$x^{2}-106x+2809=-105+2809$$

Add -105 to 2809.

$$x^{2}-106x+2809=2704$$

Factor x^{2}-106x+2809. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-53\right)^{2}=2704$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-53\right)^{2}}=\sqrt{2704}$$

Simplify.

$$x-53=52 x-53=-52$$

Add 53 to both sides of the equation.

$$x=105 x=1$$