Solve x^2+14x+49=(2x+6)(4+x)

$${ x }^{ 2 } +14x+49=(2x+6)(4+x)$$

Solve for x

$$x=5$$

$$x=-5$$

Steps by Finding Square Root

Use the distributive property to multiply 2x+6 by 4+x and combine like terms.

$$x^{2}+14x+49=14x+2x^{2}+24$$

Subtract 14x from both sides.

$$x^{2}+14x+49-14x=2x^{2}+24$$

Combine 14x and -14x to get 0.

$$x^{2}+49=2x^{2}+24$$

Subtract 2x^{2} from both sides.

$$x^{2}+49-2x^{2}=24$$

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

$$-x^{2}+49=24$$

Subtract 49 from both sides.

$$-x^{2}=24-49$$

Subtract 49 from 24 to get -25.

$$-x^{2}=-25$$

Divide both sides by -1.

$$x^{2}=\frac{-25}{-1}$$

Fraction \frac{-25}{-1} can be simplified to 25 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=25$$

Take the square root of both sides of the equation.

$$x=5 x=-5$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x+6 by 4+x and combine like terms.

$$x^{2}+14x+49=14x+2x^{2}+24$$

Subtract 14x from both sides.

$$x^{2}+14x+49-14x=2x^{2}+24$$

Combine 14x and -14x to get 0.

$$x^{2}+49=2x^{2}+24$$

Subtract 2x^{2} from both sides.

$$x^{2}+49-2x^{2}=24$$

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

$$-x^{2}+49=24$$

Subtract 24 from both sides.

$$-x^{2}+49-24=0$$

Subtract 24 from 49 to get 25.

$$-x^{2}+25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 25}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 25}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 25}}{2\left(-1\right)}$$

Multiply 4 times 25.

$$x=\frac{0±\sqrt{100}}{2\left(-1\right)}$$

Take the square root of 100.

$$x=\frac{0±10}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±10}{-2}$$

Now solve the equation x=\frac{0±10}{-2} when ± is plus. Divide 10 by -2.

$$x=-5$$

Now solve the equation x=\frac{0±10}{-2} when ± is minus. Divide -10 by -2.

$$x=5$$

The equation is now solved.

$$x=-5 x=5$$