Solve 3(x+1)^2-(2x+1)^2=2x-14

$$3 ( x + 1 ) ^ { 2 } - ( 2 x + 1 ) ^ { 2 } = 2 x - 14$$

Solve for x

$$x=4$$

$$x=-4$$

Steps by Finding Square Root

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$3\left(x^{2}+2x+1\right)-\left(2x+1\right)^{2}=2x-14$$

Use the distributive property to multiply 3 by x^{2}+2x+1.

$$3x^{2}+6x+3-\left(2x+1\right)^{2}=2x-14$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.

$$3x^{2}+6x+3-\left(4x^{2}+4x+1\right)=2x-14$$

To find the opposite of 4x^{2}+4x+1, find the opposite of each term.

$$3x^{2}+6x+3-4x^{2}-4x-1=2x-14$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$-x^{2}+6x+3-4x-1=2x-14$$

Combine 6x and -4x to get 2x.

$$-x^{2}+2x+3-1=2x-14$$

Subtract 1 from 3 to get 2.

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

Subtract 2x from both sides.

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

Combine 2x and -2x to get 0.

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

Subtract 2 from both sides.

$$-x^{2}=-14-2$$

Subtract 2 from -14 to get -16.

$$-x^{2}=-16$$

Divide both sides by -1.

$$x^{2}=\frac{-16}{-1}$$

Fraction \frac{-16}{-1} can be simplified to 16 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$3\left(x^{2}+2x+1\right)-\left(2x+1\right)^{2}=2x-14$$

Use the distributive property to multiply 3 by x^{2}+2x+1.

$$3x^{2}+6x+3-\left(2x+1\right)^{2}=2x-14$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.

$$3x^{2}+6x+3-\left(4x^{2}+4x+1\right)=2x-14$$

To find the opposite of 4x^{2}+4x+1, find the opposite of each term.

$$3x^{2}+6x+3-4x^{2}-4x-1=2x-14$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$-x^{2}+6x+3-4x-1=2x-14$$

Combine 6x and -4x to get 2x.

$$-x^{2}+2x+3-1=2x-14$$

Subtract 1 from 3 to get 2.

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

Subtract 2x from both sides.

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

Combine 2x and -2x to get 0.

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

Add 14 to both sides.

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

Add 2 and 14 to get 16.

$$-x^{2}+16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 16}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 16}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 16}}{2\left(-1\right)}$$

Multiply 4 times 16.

$$x=\frac{0±\sqrt{64}}{2\left(-1\right)}$$

Take the square root of 64.

$$x=\frac{0±8}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±8}{-2}$$

Now solve the equation x=\frac{0±8}{-2} when ± is plus. Divide 8 by -2.

$$x=-4$$

Now solve the equation x=\frac{0±8}{-2} when ± is minus. Divide -8 by -2.

$$x=4$$

The equation is now solved.

$$x=-4 x=4$$