Solve 2x+7x^2-3

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

Factor

$$7\left(x-\frac{-\sqrt{22}-1}{7}\right)\left(x-\frac{\sqrt{22}-1}{7}\right)$$

Steps Using the Quadratic Formula

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.

$$7x^{2}+2x-3=0$$

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.

$$x=\frac{-2±\sqrt{2^{2}-4\times 7\left(-3\right)}}{2\times 7}$$

Square 2.

$$x=\frac{-2±\sqrt{4-4\times 7\left(-3\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{-2±\sqrt{4-28\left(-3\right)}}{2\times 7}$$

Multiply -28 times -3.

$$x=\frac{-2±\sqrt{4+84}}{2\times 7}$$

Add 4 to 84.

$$x=\frac{-2±\sqrt{88}}{2\times 7}$$

Take the square root of 88.

$$x=\frac{-2±2\sqrt{22}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{-2±2\sqrt{22}}{14}$$

Now solve the equation x=\frac{-2±2\sqrt{22}}{14} when ± is plus. Add -2 to 2\sqrt{22}.

$$x=\frac{2\sqrt{22}-2}{14}$$

Divide -2+2\sqrt{22} by 14.

$$x=\frac{\sqrt{22}-1}{7}$$

Now solve the equation x=\frac{-2±2\sqrt{22}}{14} when ± is minus. Subtract 2\sqrt{22} from -2.

$$x=\frac{-2\sqrt{22}-2}{14}$$

Divide -2-2\sqrt{22} by 14.

$$x=\frac{-\sqrt{22}-1}{7}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-1+\sqrt{22}}{7} for x_{1} and \frac{-1-\sqrt{22}}{7} for x_{2}.

$$7x^{2}+2x-3=7\left(x-\frac{\sqrt{22}-1}{7}\right)\left(x-\frac{-\sqrt{22}-1}{7}\right)$$

Evaluate

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