Solve 4*2x^2-4+3*x^2+3*x

$$4 \times 2 { x }^{ 2 } -4+3 \times { x }^{ 2 } +3 \times x$$

Evaluate

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

Solution Steps

Multiply 4 and 2 to get 8.

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

Combine 8x^{2} and 3x^{2} to get 11x^{2}.

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

Factor

$$11\left(x-\frac{-\sqrt{185}-3}{22}\right)\left(x-\frac{\sqrt{185}-3}{22}\right)$$

Steps Using the Quadratic Formula

Multiply 4 and 2 to get 8.

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

Combine 8x^{2} and 3x^{2} to get 11x^{2}.

$$factor(11x^{2}-4+3x)$$

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.

$$11x^{2}+3x-4=0$$

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.

$$x=\frac{-3±\sqrt{3^{2}-4\times 11\left(-4\right)}}{2\times 11}$$

Square 3.

$$x=\frac{-3±\sqrt{9-4\times 11\left(-4\right)}}{2\times 11}$$

Multiply -4 times 11.

$$x=\frac{-3±\sqrt{9-44\left(-4\right)}}{2\times 11}$$

Multiply -44 times -4.

$$x=\frac{-3±\sqrt{9+176}}{2\times 11}$$

Add 9 to 176.

$$x=\frac{-3±\sqrt{185}}{2\times 11}$$

Multiply 2 times 11.

$$x=\frac{-3±\sqrt{185}}{22}$$

Now solve the equation x=\frac{-3±\sqrt{185}}{22} when ± is plus. Add -3 to \sqrt{185}.

$$x=\frac{\sqrt{185}-3}{22}$$

Now solve the equation x=\frac{-3±\sqrt{185}}{22} when ± is minus. Subtract \sqrt{185} from -3.

$$x=\frac{-\sqrt{185}-3}{22}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-3+\sqrt{185}}{22} for x_{1} and \frac{-3-\sqrt{185}}{22} for x_{2}.

$$11x^{2}+3x-4=11\left(x-\frac{\sqrt{185}-3}{22}\right)\left(x-\frac{-\sqrt{185}-3}{22}\right)$$