Solve 3x^2+10x-3+18x+2

$$3 { x }^{ 2 } +10x-3+18x+2$$

Evaluate

$$3x^{2}+28x-1$$

Solution Steps

Combine 10x and 18x to get 28x.

$$3x^{2}+28x-3+2$$

Add -3 and 2 to get -1.

$$3x^{2}+28x-1$$

Factor

$$3\left(x-\frac{-\sqrt{199}-14}{3}\right)\left(x-\frac{\sqrt{199}-14}{3}\right)$$

Steps Using the Quadratic Formula

Combine 10x and 18x to get 28x.

$$factor(3x^{2}+28x-3+2)$$

Add -3 and 2 to get -1.

$$factor(3x^{2}+28x-1)$$

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.

$$3x^{2}+28x-1=0$$

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.

$$x=\frac{-28±\sqrt{28^{2}-4\times 3\left(-1\right)}}{2\times 3}$$

Square 28.

$$x=\frac{-28±\sqrt{784-4\times 3\left(-1\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{-28±\sqrt{784-12\left(-1\right)}}{2\times 3}$$

Multiply -12 times -1.

$$x=\frac{-28±\sqrt{784+12}}{2\times 3}$$

Add 784 to 12.

$$x=\frac{-28±\sqrt{796}}{2\times 3}$$

Take the square root of 796.

$$x=\frac{-28±2\sqrt{199}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{-28±2\sqrt{199}}{6}$$

Now solve the equation x=\frac{-28±2\sqrt{199}}{6} when ± is plus. Add -28 to 2\sqrt{199}.

$$x=\frac{2\sqrt{199}-28}{6}$$

Divide -28+2\sqrt{199} by 6.

$$x=\frac{\sqrt{199}-14}{3}$$

Now solve the equation x=\frac{-28±2\sqrt{199}}{6} when ± is minus. Subtract 2\sqrt{199} from -28.

$$x=\frac{-2\sqrt{199}-28}{6}$$

Divide -28-2\sqrt{199} by 6.

$$x=\frac{-\sqrt{199}-14}{3}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-14+\sqrt{199}}{3} for x_{1} and \frac{-14-\sqrt{199}}{3} for x_{2}.

$$3x^{2}+28x-1=3\left(x-\frac{\sqrt{199}-14}{3}\right)\left(x-\frac{-\sqrt{199}-14}{3}\right)$$