Solve 2x-(x+1)^2=3x^2-5

$$2 x - ( x + 1 ) ^ { 2 } = 3 x ^ { 2 } - 5$$

Solve for x

$$x=1$$

$$x=-1$$

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}.

$$2x-\left(x^{2}+2x+1\right)=3x^{2}-5$$

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

$$2x-x^{2}-2x-1=3x^{2}-5$$

Combine 2x and -2x to get 0.

$$-x^{2}-1=3x^{2}-5$$

Subtract 3x^{2} from both sides.

$$-x^{2}-1-3x^{2}=-5$$

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

$$-4x^{2}-1=-5$$

Add 1 to both sides.

$$-4x^{2}=-5+1$$

Add -5 and 1 to get -4.

$$-4x^{2}=-4$$

Divide both sides by -4.

$$x^{2}=\frac{-4}{-4}$$

Divide -4 by -4 to get 1.

$$x^{2}=1$$

Take the square root of both sides of the equation.

$$x=1 x=-1$$

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}.

$$2x-\left(x^{2}+2x+1\right)=3x^{2}-5$$

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

$$2x-x^{2}-2x-1=3x^{2}-5$$

Combine 2x and -2x to get 0.

$$-x^{2}-1=3x^{2}-5$$

Subtract 3x^{2} from both sides.

$$-x^{2}-1-3x^{2}=-5$$

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

$$-4x^{2}-1=-5$$

Add 5 to both sides.

$$-4x^{2}-1+5=0$$

Add -1 and 5 to get 4.

$$-4x^{2}+4=0$$

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

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

Square 0.

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

Multiply -4 times -4.

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

Multiply 16 times 4.

$$x=\frac{0±\sqrt{64}}{2\left(-4\right)}$$

Take the square root of 64.

$$x=\frac{0±8}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±8}{-8}$$

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

$$x=-1$$

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

$$x=1$$

The equation is now solved.

$$x=-1 x=1$$