Solve 8x-48+10x^2

$$8 x - 48 + 10 x ^ { 2 }$$

Factor

$$10\left(x-\frac{-2\sqrt{31}-2}{5}\right)\left(x-\frac{2\sqrt{31}-2}{5}\right)$$

Steps Using the Quadratic Formula

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.

$$10x^{2}+8x-48=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\times 10\left(-48\right)}}{2\times 10}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\times 10\left(-48\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{-8±\sqrt{64-40\left(-48\right)}}{2\times 10}$$

Multiply -40 times -48.

$$x=\frac{-8±\sqrt{64+1920}}{2\times 10}$$

Add 64 to 1920.

$$x=\frac{-8±\sqrt{1984}}{2\times 10}$$

Take the square root of 1984.

$$x=\frac{-8±8\sqrt{31}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{-8±8\sqrt{31}}{20}$$

Now solve the equation x=\frac{-8±8\sqrt{31}}{20} when ± is plus. Add -8 to 8\sqrt{31}.

$$x=\frac{8\sqrt{31}-8}{20}$$

Divide -8+8\sqrt{31} by 20.

$$x=\frac{2\sqrt{31}-2}{5}$$

Now solve the equation x=\frac{-8±8\sqrt{31}}{20} when ± is minus. Subtract 8\sqrt{31} from -8.

$$x=\frac{-8\sqrt{31}-8}{20}$$

Divide -8-8\sqrt{31} by 20.

$$x=\frac{-2\sqrt{31}-2}{5}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-2+2\sqrt{31}}{5} for x_{1} and \frac{-2-2\sqrt{31}}{5} for x_{2}.

$$10x^{2}+8x-48=10\left(x-\frac{2\sqrt{31}-2}{5}\right)\left(x-\frac{-2\sqrt{31}-2}{5}\right)$$

Evaluate

$$10x^{2}+8x-48$$