Solve 8y^2-7y+5-4y-7

$$8 y ^ { 2 } - 7 y + 5 - 4 y - 7$$

Evaluate

$$8y^{2}-11y-2$$

Solution Steps

Combine -7y and -4y to get -11y.

$$8y^{2}-11y+5-7$$

Subtract 7 from 5 to get -2.

$$8y^{2}-11y-2$$

Factor

$$8\left(y-\frac{11-\sqrt{185}}{16}\right)\left(y-\frac{\sqrt{185}+11}{16}\right)$$

Steps Using the Quadratic Formula

Combine -7y and -4y to get -11y.

$$factor(8y^{2}-11y+5-7)$$

Subtract 7 from 5 to get -2.

$$factor(8y^{2}-11y-2)$$

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.

$$8y^{2}-11y-2=0$$

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.

$$y=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 8\left(-2\right)}}{2\times 8}$$

Square -11.

$$y=\frac{-\left(-11\right)±\sqrt{121-4\times 8\left(-2\right)}}{2\times 8}$$

Multiply -4 times 8.

$$y=\frac{-\left(-11\right)±\sqrt{121-32\left(-2\right)}}{2\times 8}$$

Multiply -32 times -2.

$$y=\frac{-\left(-11\right)±\sqrt{121+64}}{2\times 8}$$

Add 121 to 64.

$$y=\frac{-\left(-11\right)±\sqrt{185}}{2\times 8}$$

The opposite of -11 is 11.

$$y=\frac{11±\sqrt{185}}{2\times 8}$$

Multiply 2 times 8.

$$y=\frac{11±\sqrt{185}}{16}$$

Now solve the equation y=\frac{11±\sqrt{185}}{16} when ± is plus. Add 11 to \sqrt{185}.

$$y=\frac{\sqrt{185}+11}{16}$$

Now solve the equation y=\frac{11±\sqrt{185}}{16} when ± is minus. Subtract \sqrt{185} from 11.

$$y=\frac{11-\sqrt{185}}{16}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{11+\sqrt{185}}{16} for x_{1} and \frac{11-\sqrt{185}}{16} for x_{2}.

$$8y^{2}-11y-2=8\left(y-\frac{\sqrt{185}+11}{16}\right)\left(y-\frac{11-\sqrt{185}}{16}\right)$$