Solve 9x^2+2x-1-2x^2-9

$$9 { x }^{ 2 } +2x-1-2 { x }^{ 2 } -9$$

Evaluate

$$7x^{2}+2x-10$$

Solution Steps

Combine 9x^{2} and -2x^{2} to get 7x^{2}.

$$7x^{2}+2x-1-9$$

Subtract 9 from -1 to get -10.

$$7x^{2}+2x-10$$

Factor

$$7\left(x-\frac{-\sqrt{71}-1}{7}\right)\left(x-\frac{\sqrt{71}-1}{7}\right)$$

Steps Using the Quadratic Formula

Combine 9x^{2} and -2x^{2} to get 7x^{2}.

$$factor(7x^{2}+2x-1-9)$$

Subtract 9 from -1 to get -10.

$$factor(7x^{2}+2x-10)$$

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.

$$7x^{2}+2x-10=0$$

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.

$$x=\frac{-2±\sqrt{2^{2}-4\times 7\left(-10\right)}}{2\times 7}$$

Square 2.

$$x=\frac{-2±\sqrt{4-4\times 7\left(-10\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{-2±\sqrt{4-28\left(-10\right)}}{2\times 7}$$

Multiply -28 times -10.

$$x=\frac{-2±\sqrt{4+280}}{2\times 7}$$

Add 4 to 280.

$$x=\frac{-2±\sqrt{284}}{2\times 7}$$

Take the square root of 284.

$$x=\frac{-2±2\sqrt{71}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{-2±2\sqrt{71}}{14}$$

Now solve the equation x=\frac{-2±2\sqrt{71}}{14} when ± is plus. Add -2 to 2\sqrt{71}.

$$x=\frac{2\sqrt{71}-2}{14}$$

Divide -2+2\sqrt{71} by 14.

$$x=\frac{\sqrt{71}-1}{7}$$

Now solve the equation x=\frac{-2±2\sqrt{71}}{14} when ± is minus. Subtract 2\sqrt{71} from -2.

$$x=\frac{-2\sqrt{71}-2}{14}$$

Divide -2-2\sqrt{71} by 14.

$$x=\frac{-\sqrt{71}-1}{7}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-1+\sqrt{71}}{7} for x_{1} and \frac{-1-\sqrt{71}}{7} for x_{2}.

$$7x^{2}+2x-10=7\left(x-\frac{\sqrt{71}-1}{7}\right)\left(x-\frac{-\sqrt{71}-1}{7}\right)$$