Solve 2*x^2-2*7x-15

$$2 \cdot x ^ { 2 } - 2 \cdot 7 x - 15$$

Factor

$$2\left(x-\frac{7-\sqrt{79}}{2}\right)\left(x-\frac{\sqrt{79}+7}{2}\right)$$

Steps Using the Quadratic Formula

Multiply 2 and 7 to get 14.

$$factor(2x^{2}-14x-15)$$

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.

$$2x^{2}-14x-15=0$$

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.

$$x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 2\left(-15\right)}}{2\times 2}$$

Square -14.

$$x=\frac{-\left(-14\right)±\sqrt{196-4\times 2\left(-15\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-14\right)±\sqrt{196-8\left(-15\right)}}{2\times 2}$$

Multiply -8 times -15.

$$x=\frac{-\left(-14\right)±\sqrt{196+120}}{2\times 2}$$

Add 196 to 120.

$$x=\frac{-\left(-14\right)±\sqrt{316}}{2\times 2}$$

Take the square root of 316.

$$x=\frac{-\left(-14\right)±2\sqrt{79}}{2\times 2}$$

The opposite of -14 is 14.

$$x=\frac{14±2\sqrt{79}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{14±2\sqrt{79}}{4}$$

Now solve the equation x=\frac{14±2\sqrt{79}}{4} when ± is plus. Add 14 to 2\sqrt{79}.

$$x=\frac{2\sqrt{79}+14}{4}$$

Divide 14+2\sqrt{79} by 4.

$$x=\frac{\sqrt{79}+7}{2}$$

Now solve the equation x=\frac{14±2\sqrt{79}}{4} when ± is minus. Subtract 2\sqrt{79} from 14.

$$x=\frac{14-2\sqrt{79}}{4}$$

Divide 14-2\sqrt{79} by 4.

$$x=\frac{7-\sqrt{79}}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{7+\sqrt{79}}{2} for x_{1} and \frac{7-\sqrt{79}}{2} for x_{2}.

$$2x^{2}-14x-15=2\left(x-\frac{\sqrt{79}+7}{2}\right)\left(x-\frac{7-\sqrt{79}}{2}\right)$$

Evaluate

$$2x^{2}-14x-15$$

Solution Steps

Multiply 2 and 7 to get 14.

$$2x^{2}-14x-15$$