Solve 2y^2+28y-90

$$2 { y }^{ 2 } +28y-90$$

Factor

$$2\left(y-\left(-\sqrt{94}-7\right)\right)\left(y-\left(\sqrt{94}-7\right)\right)$$

Steps Using the Quadratic Formula

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.

$$2y^{2}+28y-90=0$$

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.

$$y=\frac{-28±\sqrt{28^{2}-4\times 2\left(-90\right)}}{2\times 2}$$

Square 28.

$$y=\frac{-28±\sqrt{784-4\times 2\left(-90\right)}}{2\times 2}$$

Multiply -4 times 2.

$$y=\frac{-28±\sqrt{784-8\left(-90\right)}}{2\times 2}$$

Multiply -8 times -90.

$$y=\frac{-28±\sqrt{784+720}}{2\times 2}$$

Add 784 to 720.

$$y=\frac{-28±\sqrt{1504}}{2\times 2}$$

Take the square root of 1504.

$$y=\frac{-28±4\sqrt{94}}{2\times 2}$$

Multiply 2 times 2.

$$y=\frac{-28±4\sqrt{94}}{4}$$

Now solve the equation y=\frac{-28±4\sqrt{94}}{4} when ± is plus. Add -28 to 4\sqrt{94}.

$$y=\frac{4\sqrt{94}-28}{4}$$

Divide -28+4\sqrt{94} by 4.

$$y=\sqrt{94}-7$$

Now solve the equation y=\frac{-28±4\sqrt{94}}{4} when ± is minus. Subtract 4\sqrt{94} from -28.

$$y=\frac{-4\sqrt{94}-28}{4}$$

Divide -28-4\sqrt{94} by 4.

$$y=-\sqrt{94}-7$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -7+\sqrt{94} for x_{1} and -7-\sqrt{94} for x_{2}.

$$2y^{2}+28y-90=2\left(y-\left(\sqrt{94}-7\right)\right)\left(y-\left(-\sqrt{94}-7\right)\right)$$

Evaluate

$$2\left(y^{2}+14y-45\right)$$