Solve 22x-48+x^2(4

$$22 x - 48 + x ^ { 2 } ( 4$$

Factor

$$4\left(x-\frac{-\sqrt{313}-11}{4}\right)\left(x-\frac{\sqrt{313}-11}{4}\right)$$

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.

$$4x^{2}+22x-48=0$$

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.

$$x=\frac{-22±\sqrt{22^{2}-4\times 4\left(-48\right)}}{2\times 4}$$

Square 22.

$$x=\frac{-22±\sqrt{484-4\times 4\left(-48\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-22±\sqrt{484-16\left(-48\right)}}{2\times 4}$$

Multiply -16 times -48.

$$x=\frac{-22±\sqrt{484+768}}{2\times 4}$$

Add 484 to 768.

$$x=\frac{-22±\sqrt{1252}}{2\times 4}$$

Take the square root of 1252.

$$x=\frac{-22±2\sqrt{313}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{-22±2\sqrt{313}}{8}$$

Now solve the equation x=\frac{-22±2\sqrt{313}}{8} when ± is plus. Add -22 to 2\sqrt{313}.

$$x=\frac{2\sqrt{313}-22}{8}$$

Divide -22+2\sqrt{313} by 8.

$$x=\frac{\sqrt{313}-11}{4}$$

Now solve the equation x=\frac{-22±2\sqrt{313}}{8} when ± is minus. Subtract 2\sqrt{313} from -22.

$$x=\frac{-2\sqrt{313}-22}{8}$$

Divide -22-2\sqrt{313} by 8.

$$x=\frac{-\sqrt{313}-11}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-11+\sqrt{313}}{4} for x_{1} and \frac{-11-\sqrt{313}}{4} for x_{2}.

$$4x^{2}+22x-48=4\left(x-\frac{\sqrt{313}-11}{4}\right)\left(x-\frac{-\sqrt{313}-11}{4}\right)$$

Evaluate

$$4x^{2}+22x-48$$