Solve 15(15+17)=x(x+14)

$$15(15+17)=x(x+14)$$

Solve for x

$$x=-30$$

$$x=16$$

Steps Using the Quadratic Formula

Add 15 and 17 to get 32.

$$15\times 32=x\left(x+14\right)$$

Multiply 15 and 32 to get 480.

$$480=x\left(x+14\right)$$

Use the distributive property to multiply x by x+14.

$$480=x^{2}+14x$$

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

$$x^{2}+14x=480$$

Subtract 480 from both sides.

$$x^{2}+14x-480=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 14 for b, and -480 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-14±\sqrt{14^{2}-4\left(-480\right)}}{2}$$

Square 14.

$$x=\frac{-14±\sqrt{196-4\left(-480\right)}}{2}$$

Multiply -4 times -480.

$$x=\frac{-14±\sqrt{196+1920}}{2}$$

Add 196 to 1920.

$$x=\frac{-14±\sqrt{2116}}{2}$$

Take the square root of 2116.

$$x=\frac{-14±46}{2}$$

Now solve the equation x=\frac{-14±46}{2} when ± is plus. Add -14 to 46.

$$x=\frac{32}{2}$$

Divide 32 by 2.

$$x=16$$

Now solve the equation x=\frac{-14±46}{2} when ± is minus. Subtract 46 from -14.

$$x=-\frac{60}{2}$$

Divide -60 by 2.

$$x=-30$$

The equation is now solved.

$$x=16 x=-30$$

Steps for Completing the Square

Add 15 and 17 to get 32.

$$15\times 32=x\left(x+14\right)$$

Multiply 15 and 32 to get 480.

$$480=x\left(x+14\right)$$

Use the distributive property to multiply x by x+14.

$$480=x^{2}+14x$$

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

$$x^{2}+14x=480$$

Divide 14, the coefficient of the x term, by 2 to get 7. Then add the square of 7 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+14x+7^{2}=480+7^{2}$$

Square 7.

$$x^{2}+14x+49=480+49$$

Add 480 to 49.

$$x^{2}+14x+49=529$$

Factor x^{2}+14x+49. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+7\right)^{2}=529$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+7\right)^{2}}=\sqrt{529}$$

Simplify.

$$x+7=23 x+7=-23$$

Subtract 7 from both sides of the equation.

$$x=16 x=-30$$