Solve 3x^2+4x-8-2x^2+4x+2

$$3 x ^ { 2 } + 4 x - 8 - 2 x ^ { 2 } + 4 x + 2$$

Evaluate

$$x^{2}+8x-6$$

Solution Steps

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

$$x^{2}+4x-8+4x+2$$

Combine 4x and 4x to get 8x.

$$x^{2}+8x-8+2$$

Add -8 and 2 to get -6.

$$x^{2}+8x-6$$

Factor

$$\left(x-\left(-\sqrt{22}-4\right)\right)\left(x-\left(\sqrt{22}-4\right)\right)$$

Steps Using the Quadratic Formula

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

$$factor(x^{2}+4x-8+4x+2)$$

Combine 4x and 4x to get 8x.

$$factor(x^{2}+8x-8+2)$$

Add -8 and 2 to get -6.

$$factor(x^{2}+8x-6)$$

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$x^{2}+8x-6=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-6\right)}}{2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-6\right)}}{2}$$

Multiply -4 times -6.

$$x=\frac{-8±\sqrt{64+24}}{2}$$

Add 64 to 24.

$$x=\frac{-8±\sqrt{88}}{2}$$

Take the square root of 88.

$$x=\frac{-8±2\sqrt{22}}{2}$$

Now solve the equation x=\frac{-8±2\sqrt{22}}{2} when ± is plus. Add -8 to 2\sqrt{22}.

$$x=\frac{2\sqrt{22}-8}{2}$$

Divide -8+2\sqrt{22} by 2.

$$x=\sqrt{22}-4$$

Now solve the equation x=\frac{-8±2\sqrt{22}}{2} when ± is minus. Subtract 2\sqrt{22} from -8.

$$x=\frac{-2\sqrt{22}-8}{2}$$

Divide -8-2\sqrt{22} by 2.

$$x=-\sqrt{22}-4$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -4+\sqrt{22} for x_{1} and -4-\sqrt{22} for x_{2}.

$$x^{2}+8x-6=\left(x-\left(\sqrt{22}-4\right)\right)\left(x-\left(-\sqrt{22}-4\right)\right)$$