Solve 10x+3x^2-8+12x+15x+4

$$10 x + 3 x ^ { 2 } - 8 + 12 x + 15 x + 4$$

Evaluate

$$3x^{2}+37x-4$$

Solution Steps

Combine 10x and 12x to get 22x.

$$22x+3x^{2}-8+15x+4$$

Combine 22x and 15x to get 37x.

$$37x+3x^{2}-8+4$$

Add -8 and 4 to get -4.

$$37x+3x^{2}-4$$

Factor

$$3\left(x-\frac{-\sqrt{1417}-37}{6}\right)\left(x-\frac{\sqrt{1417}-37}{6}\right)$$

Steps Using the Quadratic Formula

Combine 10x and 12x to get 22x.

$$factor(22x+3x^{2}-8+15x+4)$$

Combine 22x and 15x to get 37x.

$$factor(37x+3x^{2}-8+4)$$

Add -8 and 4 to get -4.

$$factor(37x+3x^{2}-4)$$

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.

$$3x^{2}+37x-4=0$$

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.

$$x=\frac{-37±\sqrt{37^{2}-4\times 3\left(-4\right)}}{2\times 3}$$

Square 37.

$$x=\frac{-37±\sqrt{1369-4\times 3\left(-4\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{-37±\sqrt{1369-12\left(-4\right)}}{2\times 3}$$

Multiply -12 times -4.

$$x=\frac{-37±\sqrt{1369+48}}{2\times 3}$$

Add 1369 to 48.

$$x=\frac{-37±\sqrt{1417}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{-37±\sqrt{1417}}{6}$$

Now solve the equation x=\frac{-37±\sqrt{1417}}{6} when ± is plus. Add -37 to \sqrt{1417}.

$$x=\frac{\sqrt{1417}-37}{6}$$

Now solve the equation x=\frac{-37±\sqrt{1417}}{6} when ± is minus. Subtract \sqrt{1417} from -37.

$$x=\frac{-\sqrt{1417}-37}{6}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-37+\sqrt{1417}}{6} for x_{1} and \frac{-37-\sqrt{1417}}{6} for x_{2}.

$$3x^{2}+37x-4=3\left(x-\frac{\sqrt{1417}-37}{6}\right)\left(x-\frac{-\sqrt{1417}-37}{6}\right)$$