Solve 3x^2+4x-7-x+11x^2-9+x

$$3 { x }^{ 2 } +4x-7-x+11 { x }^{ 2 } -9+x$$

Evaluate

$$14x^{2}+4x-16$$

Solution Steps

Combine 4x and -x to get 3x.

$$3x^{2}+3x-7+11x^{2}-9+x$$

Combine 3x^{2} and 11x^{2} to get 14x^{2}.

$$14x^{2}+3x-7-9+x$$

Subtract 9 from -7 to get -16.

$$14x^{2}+3x-16+x$$

Combine 3x and x to get 4x.

$$14x^{2}+4x-16$$

Factor

$$14\left(x-\frac{-\sqrt{57}-1}{7}\right)\left(x-\frac{\sqrt{57}-1}{7}\right)$$

Steps Using the Quadratic Formula

Combine 4x and -x to get 3x.

$$factor(3x^{2}+3x-7+11x^{2}-9+x)$$

Combine 3x^{2} and 11x^{2} to get 14x^{2}.

$$factor(14x^{2}+3x-7-9+x)$$

Subtract 9 from -7 to get -16.

$$factor(14x^{2}+3x-16+x)$$

Combine 3x and x to get 4x.

$$factor(14x^{2}+4x-16)$$

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.

$$14x^{2}+4x-16=0$$

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.

$$x=\frac{-4±\sqrt{4^{2}-4\times 14\left(-16\right)}}{2\times 14}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\times 14\left(-16\right)}}{2\times 14}$$

Multiply -4 times 14.

$$x=\frac{-4±\sqrt{16-56\left(-16\right)}}{2\times 14}$$

Multiply -56 times -16.

$$x=\frac{-4±\sqrt{16+896}}{2\times 14}$$

Add 16 to 896.

$$x=\frac{-4±\sqrt{912}}{2\times 14}$$

Take the square root of 912.

$$x=\frac{-4±4\sqrt{57}}{2\times 14}$$

Multiply 2 times 14.

$$x=\frac{-4±4\sqrt{57}}{28}$$

Now solve the equation x=\frac{-4±4\sqrt{57}}{28} when ± is plus. Add -4 to 4\sqrt{57}.

$$x=\frac{4\sqrt{57}-4}{28}$$

Divide -4+4\sqrt{57} by 28.

$$x=\frac{\sqrt{57}-1}{7}$$

Now solve the equation x=\frac{-4±4\sqrt{57}}{28} when ± is minus. Subtract 4\sqrt{57} from -4.

$$x=\frac{-4\sqrt{57}-4}{28}$$

Divide -4-4\sqrt{57} by 28.

$$x=\frac{-\sqrt{57}-1}{7}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-1+\sqrt{57}}{7} for x_{1} and \frac{-1-\sqrt{57}}{7} for x_{2}.

$$14x^{2}+4x-16=14\left(x-\frac{\sqrt{57}-1}{7}\right)\left(x-\frac{-\sqrt{57}-1}{7}\right)$$