Solve (5x^2-7x-8)+(-3x-9)

$$( 5 x ^ { 2 } - 7 x - 8 ) + ( - 3 x - 9 )$$

Evaluate

$$5x^{2}-10x-17$$

Solution Steps

Combine -7x and -3x to get -10x.

$$5x^{2}-10x-8-9$$

Subtract 9 from -8 to get -17.

$$5x^{2}-10x-17$$

Factor

$$5\left(x-\left(-\frac{\sqrt{110}}{5}+1\right)\right)\left(x-\left(\frac{\sqrt{110}}{5}+1\right)\right)$$

Steps Using the Quadratic Formula

Combine -7x and -3x to get -10x.

$$factor(5x^{2}-10x-8-9)$$

Subtract 9 from -8 to get -17.

$$factor(5x^{2}-10x-17)$$

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.

$$5x^{2}-10x-17=0$$

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.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 5\left(-17\right)}}{2\times 5}$$

Square -10.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\times 5\left(-17\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{-\left(-10\right)±\sqrt{100-20\left(-17\right)}}{2\times 5}$$

Multiply -20 times -17.

$$x=\frac{-\left(-10\right)±\sqrt{100+340}}{2\times 5}$$

Add 100 to 340.

$$x=\frac{-\left(-10\right)±\sqrt{440}}{2\times 5}$$

Take the square root of 440.

$$x=\frac{-\left(-10\right)±2\sqrt{110}}{2\times 5}$$

The opposite of -10 is 10.

$$x=\frac{10±2\sqrt{110}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{10±2\sqrt{110}}{10}$$

Now solve the equation x=\frac{10±2\sqrt{110}}{10} when ± is plus. Add 10 to 2\sqrt{110}.

$$x=\frac{2\sqrt{110}+10}{10}$$

Divide 10+2\sqrt{110} by 10.

$$x=\frac{\sqrt{110}}{5}+1$$

Now solve the equation x=\frac{10±2\sqrt{110}}{10} when ± is minus. Subtract 2\sqrt{110} from 10.

$$x=\frac{10-2\sqrt{110}}{10}$$

Divide 10-2\sqrt{110} by 10.

$$x=-\frac{\sqrt{110}}{5}+1$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 1+\frac{\sqrt{110}}{5} for x_{1} and 1-\frac{\sqrt{110}}{5} for x_{2}.

$$5x^{2}-10x-17=5\left(x-\left(\frac{\sqrt{110}}{5}+1\right)\right)\left(x-\left(-\frac{\sqrt{110}}{5}+1\right)\right)$$