Solve 7x^2-8x-9+5x

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

Factor

$$7\left(x-\frac{3-3\sqrt{29}}{14}\right)\left(x-\frac{3\sqrt{29}+3}{14}\right)$$

Steps Using the Quadratic Formula

Combine -8x and 5x to get -3x.

$$factor(7x^{2}-3x-9)$$

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.

$$7x^{2}-3x-9=0$$

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.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 7\left(-9\right)}}{2\times 7}$$

Square -3.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\times 7\left(-9\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{-\left(-3\right)±\sqrt{9-28\left(-9\right)}}{2\times 7}$$

Multiply -28 times -9.

$$x=\frac{-\left(-3\right)±\sqrt{9+252}}{2\times 7}$$

Add 9 to 252.

$$x=\frac{-\left(-3\right)±\sqrt{261}}{2\times 7}$$

Take the square root of 261.

$$x=\frac{-\left(-3\right)±3\sqrt{29}}{2\times 7}$$

The opposite of -3 is 3.

$$x=\frac{3±3\sqrt{29}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{3±3\sqrt{29}}{14}$$

Now solve the equation x=\frac{3±3\sqrt{29}}{14} when ± is plus. Add 3 to 3\sqrt{29}.

$$x=\frac{3\sqrt{29}+3}{14}$$

Now solve the equation x=\frac{3±3\sqrt{29}}{14} when ± is minus. Subtract 3\sqrt{29} from 3.

$$x=\frac{3-3\sqrt{29}}{14}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{3+3\sqrt{29}}{14} for x_{1} and \frac{3-3\sqrt{29}}{14} for x_{2}.

$$7x^{2}-3x-9=7\left(x-\frac{3\sqrt{29}+3}{14}\right)\left(x-\frac{3-3\sqrt{29}}{14}\right)$$

Evaluate

$$7x^{2}-3x-9$$

Solution Steps

Combine -8x and 5x to get -3x.

$$7x^{2}-3x-9$$