Solve 10*x^2-5x-14

$$10 \cdot x ^ { 2 } - 5 x - 14$$

Factor

$$10\left(x-\left(-\frac{3\sqrt{65}}{20}+\frac{1}{4}\right)\right)\left(x-\left(\frac{3\sqrt{65}}{20}+\frac{1}{4}\right)\right)$$

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.

$$10x^{2}-5x-14=0$$

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.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 10\left(-14\right)}}{2\times 10}$$

Square -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 10\left(-14\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{-\left(-5\right)±\sqrt{25-40\left(-14\right)}}{2\times 10}$$

Multiply -40 times -14.

$$x=\frac{-\left(-5\right)±\sqrt{25+560}}{2\times 10}$$

Add 25 to 560.

$$x=\frac{-\left(-5\right)±\sqrt{585}}{2\times 10}$$

Take the square root of 585.

$$x=\frac{-\left(-5\right)±3\sqrt{65}}{2\times 10}$$

The opposite of -5 is 5.

$$x=\frac{5±3\sqrt{65}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{5±3\sqrt{65}}{20}$$

Now solve the equation x=\frac{5±3\sqrt{65}}{20} when ± is plus. Add 5 to 3\sqrt{65}.

$$x=\frac{3\sqrt{65}+5}{20}$$

Divide 5+3\sqrt{65} by 20.

$$x=\frac{3\sqrt{65}}{20}+\frac{1}{4}$$

Now solve the equation x=\frac{5±3\sqrt{65}}{20} when ± is minus. Subtract 3\sqrt{65} from 5.

$$x=\frac{5-3\sqrt{65}}{20}$$

Divide 5-3\sqrt{65} by 20.

$$x=-\frac{3\sqrt{65}}{20}+\frac{1}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1}{4}+\frac{3\sqrt{65}}{20} for x_{1} and \frac{1}{4}-\frac{3\sqrt{65}}{20} for x_{2}.

$$10x^{2}-5x-14=10\left(x-\left(\frac{3\sqrt{65}}{20}+\frac{1}{4}\right)\right)\left(x-\left(-\frac{3\sqrt{65}}{20}+\frac{1}{4}\right)\right)$$

Evaluate

$$10x^{2}-5x-14$$