Solve (x+7-2)(x+3)=2(x)(x+7)-2

$$( x + 7 - 2 ) ( x + 3 ) = 2 ( x ) ( x + 7 ) - 2$$

Solve for x (complex solution)

$$x=\sqrt{26}-3\approx 2.099019514$$

$$x=-\left(\sqrt{26}+3\right)\approx -8.099019514$$

Steps Using the Quadratic Formula

Subtract 2 from 7 to get 5.

$$\left(x+5\right)\left(x+3\right)=2x\left(x+7\right)-2$$

Use the distributive property to multiply x+5 by x+3 and combine like terms.

$$x^{2}+8x+15=2x\left(x+7\right)-2$$

Use the distributive property to multiply 2x by x+7.

$$x^{2}+8x+15=2x^{2}+14x-2$$

Subtract 2x^{2} from both sides.

$$x^{2}+8x+15-2x^{2}=14x-2$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}+8x+15=14x-2$$

Subtract 14x from both sides.

$$-x^{2}+8x+15-14x=-2$$

Combine 8x and -14x to get -6x.

$$-x^{2}-6x+15=-2$$

Add 2 to both sides.

$$-x^{2}-6x+15+2=0$$

Add 15 and 2 to get 17.

$$-x^{2}-6x+17=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, -6 for b, and 17 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-1\right)\times 17}}{2\left(-1\right)}$$

Square -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-1\right)\times 17}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-\left(-6\right)±\sqrt{36+4\times 17}}{2\left(-1\right)}$$

Multiply 4 times 17.

$$x=\frac{-\left(-6\right)±\sqrt{36+68}}{2\left(-1\right)}$$

Add 36 to 68.

$$x=\frac{-\left(-6\right)±\sqrt{104}}{2\left(-1\right)}$$

Take the square root of 104.

$$x=\frac{-\left(-6\right)±2\sqrt{26}}{2\left(-1\right)}$$

The opposite of -6 is 6.

$$x=\frac{6±2\sqrt{26}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{6±2\sqrt{26}}{-2}$$

Now solve the equation x=\frac{6±2\sqrt{26}}{-2} when ± is plus. Add 6 to 2\sqrt{26}.

$$x=\frac{2\sqrt{26}+6}{-2}$$

Divide 6+2\sqrt{26} by -2.

$$x=-\left(\sqrt{26}+3\right)$$

Now solve the equation x=\frac{6±2\sqrt{26}}{-2} when ± is minus. Subtract 2\sqrt{26} from 6.

$$x=\frac{6-2\sqrt{26}}{-2}$$

Divide 6-2\sqrt{26} by -2.

$$x=\sqrt{26}-3$$

The equation is now solved.

$$x=-\left(\sqrt{26}+3\right) x=\sqrt{26}-3$$

Steps for Completing the Square

Subtract 2 from 7 to get 5.

$$\left(x+5\right)\left(x+3\right)=2x\left(x+7\right)-2$$

Use the distributive property to multiply x+5 by x+3 and combine like terms.

$$x^{2}+8x+15=2x\left(x+7\right)-2$$

Use the distributive property to multiply 2x by x+7.

$$x^{2}+8x+15=2x^{2}+14x-2$$

Subtract 2x^{2} from both sides.

$$x^{2}+8x+15-2x^{2}=14x-2$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}+8x+15=14x-2$$

Subtract 14x from both sides.

$$-x^{2}+8x+15-14x=-2$$

Combine 8x and -14x to get -6x.

$$-x^{2}-6x+15=-2$$

Subtract 15 from both sides.

$$-x^{2}-6x=-2-15$$

Subtract 15 from -2 to get -17.

$$-x^{2}-6x=-17$$

Divide both sides by -1.

$$\frac{-x^{2}-6x}{-1}=-\frac{17}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\left(-\frac{6}{-1}\right)x=-\frac{17}{-1}$$

Divide -6 by -1.

$$x^{2}+6x=-\frac{17}{-1}$$

Divide -17 by -1.

$$x^{2}+6x=17$$

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.

$$x^{2}+6x+3^{2}=17+3^{2}$$

Square 3.

$$x^{2}+6x+9=17+9$$

Add 17 to 9.

$$x^{2}+6x+9=26$$

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}.

$$\left(x+3\right)^{2}=26$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{26}$$

Simplify.

$$x+3=\sqrt{26} x+3=-\sqrt{26}$$

Subtract 3 from both sides of the equation.

$$x=\sqrt{26}-3 x=-\sqrt{26}-3$$

Solve for x

$$x=\sqrt{26}-3\approx 2.099019514$$

$$x=-\sqrt{26}-3\approx -8.099019514$$

Steps Using the Quadratic Formula

Subtract 2 from 7 to get 5.

$$\left(x+5\right)\left(x+3\right)=2x\left(x+7\right)-2$$

Use the distributive property to multiply x+5 by x+3 and combine like terms.

$$x^{2}+8x+15=2x\left(x+7\right)-2$$

Use the distributive property to multiply 2x by x+7.

$$x^{2}+8x+15=2x^{2}+14x-2$$

Subtract 2x^{2} from both sides.

$$x^{2}+8x+15-2x^{2}=14x-2$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}+8x+15=14x-2$$

Subtract 14x from both sides.

$$-x^{2}+8x+15-14x=-2$$

Combine 8x and -14x to get -6x.

$$-x^{2}-6x+15=-2$$

Add 2 to both sides.

$$-x^{2}-6x+15+2=0$$

Add 15 and 2 to get 17.

$$-x^{2}-6x+17=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, -6 for b, and 17 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-1\right)\times 17}}{2\left(-1\right)}$$

Square -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-1\right)\times 17}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-\left(-6\right)±\sqrt{36+4\times 17}}{2\left(-1\right)}$$

Multiply 4 times 17.

$$x=\frac{-\left(-6\right)±\sqrt{36+68}}{2\left(-1\right)}$$

Add 36 to 68.

$$x=\frac{-\left(-6\right)±\sqrt{104}}{2\left(-1\right)}$$

Take the square root of 104.

$$x=\frac{-\left(-6\right)±2\sqrt{26}}{2\left(-1\right)}$$

The opposite of -6 is 6.

$$x=\frac{6±2\sqrt{26}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{6±2\sqrt{26}}{-2}$$

Now solve the equation x=\frac{6±2\sqrt{26}}{-2} when ± is plus. Add 6 to 2\sqrt{26}.

$$x=\frac{2\sqrt{26}+6}{-2}$$

Divide 6+2\sqrt{26} by -2.

$$x=-\left(\sqrt{26}+3\right)$$

Now solve the equation x=\frac{6±2\sqrt{26}}{-2} when ± is minus. Subtract 2\sqrt{26} from 6.

$$x=\frac{6-2\sqrt{26}}{-2}$$

Divide 6-2\sqrt{26} by -2.

$$x=\sqrt{26}-3$$

The equation is now solved.

$$x=-\left(\sqrt{26}+3\right) x=\sqrt{26}-3$$

Steps for Completing the Square

Subtract 2 from 7 to get 5.

$$\left(x+5\right)\left(x+3\right)=2x\left(x+7\right)-2$$

Use the distributive property to multiply x+5 by x+3 and combine like terms.

$$x^{2}+8x+15=2x\left(x+7\right)-2$$

Use the distributive property to multiply 2x by x+7.

$$x^{2}+8x+15=2x^{2}+14x-2$$

Subtract 2x^{2} from both sides.

$$x^{2}+8x+15-2x^{2}=14x-2$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}+8x+15=14x-2$$

Subtract 14x from both sides.

$$-x^{2}+8x+15-14x=-2$$

Combine 8x and -14x to get -6x.

$$-x^{2}-6x+15=-2$$

Subtract 15 from both sides.

$$-x^{2}-6x=-2-15$$

Subtract 15 from -2 to get -17.

$$-x^{2}-6x=-17$$

Divide both sides by -1.

$$\frac{-x^{2}-6x}{-1}=-\frac{17}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\left(-\frac{6}{-1}\right)x=-\frac{17}{-1}$$

Divide -6 by -1.

$$x^{2}+6x=-\frac{17}{-1}$$

Divide -17 by -1.

$$x^{2}+6x=17$$

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.

$$x^{2}+6x+3^{2}=17+3^{2}$$

Square 3.

$$x^{2}+6x+9=17+9$$

Add 17 to 9.

$$x^{2}+6x+9=26$$

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}.

$$\left(x+3\right)^{2}=26$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{26}$$

Simplify.

$$x+3=\sqrt{26} x+3=-\sqrt{26}$$

Subtract 3 from both sides of the equation.

$$x=\sqrt{26}-3 x=-\sqrt{26}-3$$