Solve (11x+4)(11x+40)=1612

$$(11x+4)(11x+40)=1612$$

Solve for x

$$x=-6$$

$$x=2$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 11x+4 by 11x+40 and combine like terms.

$$121x^{2}+484x+160=1612$$

Subtract 1612 from both sides.

$$121x^{2}+484x+160-1612=0$$

Subtract 1612 from 160 to get -1452.

$$121x^{2}+484x-1452=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 121 for a, 484 for b, and -1452 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-484±\sqrt{484^{2}-4\times 121\left(-1452\right)}}{2\times 121}$$

Square 484.

$$x=\frac{-484±\sqrt{234256-4\times 121\left(-1452\right)}}{2\times 121}$$

Multiply -4 times 121.

$$x=\frac{-484±\sqrt{234256-484\left(-1452\right)}}{2\times 121}$$

Multiply -484 times -1452.

$$x=\frac{-484±\sqrt{234256+702768}}{2\times 121}$$

Add 234256 to 702768.

$$x=\frac{-484±\sqrt{937024}}{2\times 121}$$

Take the square root of 937024.

$$x=\frac{-484±968}{2\times 121}$$

Multiply 2 times 121.

$$x=\frac{-484±968}{242}$$

Now solve the equation x=\frac{-484±968}{242} when ± is plus. Add -484 to 968.

$$x=\frac{484}{242}$$

Divide 484 by 242.

$$x=2$$

Now solve the equation x=\frac{-484±968}{242} when ± is minus. Subtract 968 from -484.

$$x=-\frac{1452}{242}$$

Divide -1452 by 242.

$$x=-6$$

The equation is now solved.

$$x=2 x=-6$$

Steps for Completing the Square

Use the distributive property to multiply 11x+4 by 11x+40 and combine like terms.

$$121x^{2}+484x+160=1612$$

Subtract 160 from both sides.

$$121x^{2}+484x=1612-160$$

Subtract 160 from 1612 to get 1452.

$$121x^{2}+484x=1452$$

Divide both sides by 121.

$$\frac{121x^{2}+484x}{121}=\frac{1452}{121}$$

Dividing by 121 undoes the multiplication by 121.

$$x^{2}+\frac{484}{121}x=\frac{1452}{121}$$

Divide 484 by 121.

$$x^{2}+4x=\frac{1452}{121}$$

Divide 1452 by 121.

$$x^{2}+4x=12$$

Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+4x+2^{2}=12+2^{2}$$

Square 2.

$$x^{2}+4x+4=12+4$$

Add 12 to 4.

$$x^{2}+4x+4=16$$

Factor x^{2}+4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+2\right)^{2}=16$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{16}$$

Simplify.

$$x+2=4 x+2=-4$$

Subtract 2 from both sides of the equation.

$$x=2 x=-6$$