Solve (14)6x^2+x-2

$$( 14 ) 6 x ^ { 2 } + x - 2$$

Factor

$$84\left(x-\frac{-\sqrt{673}-1}{168}\right)\left(x-\frac{\sqrt{673}-1}{168}\right)$$

Steps Using the Quadratic Formula

Multiply 14 and 6 to get 84.

$$factor(84x^{2}+x-2)$$

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.

$$84x^{2}+x-2=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\times 84\left(-2\right)}}{2\times 84}$$

Square 1.

$$x=\frac{-1±\sqrt{1-4\times 84\left(-2\right)}}{2\times 84}$$

Multiply -4 times 84.

$$x=\frac{-1±\sqrt{1-336\left(-2\right)}}{2\times 84}$$

Multiply -336 times -2.

$$x=\frac{-1±\sqrt{1+672}}{2\times 84}$$

Add 1 to 672.

$$x=\frac{-1±\sqrt{673}}{2\times 84}$$

Multiply 2 times 84.

$$x=\frac{-1±\sqrt{673}}{168}$$

Now solve the equation x=\frac{-1±\sqrt{673}}{168} when ± is plus. Add -1 to \sqrt{673}.

$$x=\frac{\sqrt{673}-1}{168}$$

Now solve the equation x=\frac{-1±\sqrt{673}}{168} when ± is minus. Subtract \sqrt{673} from -1.

$$x=\frac{-\sqrt{673}-1}{168}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-1+\sqrt{673}}{168} for x_{1} and \frac{-1-\sqrt{673}}{168} for x_{2}.

$$84x^{2}+x-2=84\left(x-\frac{\sqrt{673}-1}{168}\right)\left(x-\frac{-\sqrt{673}-1}{168}\right)$$

Evaluate

$$84x^{2}+x-2$$

Solution Steps

Multiply 14 and 6 to get 84.

$$84x^{2}+x-2$$