Solve 2p^2-94+7p-6

$$2 p ^ { 2 } - 94 + 7 p - 6$$

Factor

$$2\left(p-\frac{-\sqrt{849}-7}{4}\right)\left(p-\frac{\sqrt{849}-7}{4}\right)$$

Steps Using the Quadratic Formula

Subtract 6 from -94 to get -100.

$$factor(2p^{2}-100+7p)$$

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.

$$2p^{2}+7p-100=0$$

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.

$$p=\frac{-7±\sqrt{7^{2}-4\times 2\left(-100\right)}}{2\times 2}$$

Square 7.

$$p=\frac{-7±\sqrt{49-4\times 2\left(-100\right)}}{2\times 2}$$

Multiply -4 times 2.

$$p=\frac{-7±\sqrt{49-8\left(-100\right)}}{2\times 2}$$

Multiply -8 times -100.

$$p=\frac{-7±\sqrt{49+800}}{2\times 2}$$

Add 49 to 800.

$$p=\frac{-7±\sqrt{849}}{2\times 2}$$

Multiply 2 times 2.

$$p=\frac{-7±\sqrt{849}}{4}$$

Now solve the equation p=\frac{-7±\sqrt{849}}{4} when ± is plus. Add -7 to \sqrt{849}.

$$p=\frac{\sqrt{849}-7}{4}$$

Now solve the equation p=\frac{-7±\sqrt{849}}{4} when ± is minus. Subtract \sqrt{849} from -7.

$$p=\frac{-\sqrt{849}-7}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-7+\sqrt{849}}{4} for x_{1} and \frac{-7-\sqrt{849}}{4} for x_{2}.

$$2p^{2}+7p-100=2\left(p-\frac{\sqrt{849}-7}{4}\right)\left(p-\frac{-\sqrt{849}-7}{4}\right)$$

Evaluate

$$2p^{2}+7p-100$$

Solution Steps

Subtract 6 from -94 to get -100.

$$2p^{2}-100+7p$$