Solve 55=(6+x)*x

$$55=(6+x) \times x$$

Solve for x

$$x=-11$$

$$x=5$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 6+x by x.

$$55=6x+x^{2}$$

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

$$6x+x^{2}=55$$

Subtract 55 from both sides.

$$6x+x^{2}-55=0$$

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.

$$x^{2}+6x-55=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 6 for b, and -55 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-55\right)}}{2}$$

Square 6.

$$x=\frac{-6±\sqrt{36-4\left(-55\right)}}{2}$$

Multiply -4 times -55.

$$x=\frac{-6±\sqrt{36+220}}{2}$$

Add 36 to 220.

$$x=\frac{-6±\sqrt{256}}{2}$$

Take the square root of 256.

$$x=\frac{-6±16}{2}$$

Now solve the equation x=\frac{-6±16}{2} when ± is plus. Add -6 to 16.

$$x=\frac{10}{2}$$

Divide 10 by 2.

$$x=5$$

Now solve the equation x=\frac{-6±16}{2} when ± is minus. Subtract 16 from -6.

$$x=-\frac{22}{2}$$

Divide -22 by 2.

$$x=-11$$

The equation is now solved.

$$x=5 x=-11$$

Steps for Completing the Square

Use the distributive property to multiply 6+x by x.

$$55=6x+x^{2}$$

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

$$6x+x^{2}=55$$

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.

$$x^{2}+6x=55$$

Divide 6, the coefficient of the x term, by 2 to get 3. Then add the square of 3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+6x+3^{2}=55+3^{2}$$

Square 3.

$$x^{2}+6x+9=55+9$$

Add 55 to 9.

$$x^{2}+6x+9=64$$

Factor x^{2}+6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+3\right)^{2}=64$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{64}$$

Simplify.

$$x+3=8 x+3=-8$$

Subtract 3 from both sides of the equation.

$$x=5 x=-11$$