Solve 6p^2+15p+4p-10

$$6 p ^ { 2 } + 15 p + 4 p - 10$$

Factor

$$6\left(p-\frac{-\sqrt{601}-19}{12}\right)\left(p-\frac{\sqrt{601}-19}{12}\right)$$

Steps Using the Quadratic Formula

Combine 15p and 4p to get 19p.

$$factor(6p^{2}+19p-10)$$

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.

$$6p^{2}+19p-10=0$$

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.

$$p=\frac{-19±\sqrt{19^{2}-4\times 6\left(-10\right)}}{2\times 6}$$

Square 19.

$$p=\frac{-19±\sqrt{361-4\times 6\left(-10\right)}}{2\times 6}$$

Multiply -4 times 6.

$$p=\frac{-19±\sqrt{361-24\left(-10\right)}}{2\times 6}$$

Multiply -24 times -10.

$$p=\frac{-19±\sqrt{361+240}}{2\times 6}$$

Add 361 to 240.

$$p=\frac{-19±\sqrt{601}}{2\times 6}$$

Multiply 2 times 6.

$$p=\frac{-19±\sqrt{601}}{12}$$

Now solve the equation p=\frac{-19±\sqrt{601}}{12} when ± is plus. Add -19 to \sqrt{601}.

$$p=\frac{\sqrt{601}-19}{12}$$

Now solve the equation p=\frac{-19±\sqrt{601}}{12} when ± is minus. Subtract \sqrt{601} from -19.

$$p=\frac{-\sqrt{601}-19}{12}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-19+\sqrt{601}}{12} for x_{1} and \frac{-19-\sqrt{601}}{12} for x_{2}.

$$6p^{2}+19p-10=6\left(p-\frac{\sqrt{601}-19}{12}\right)\left(p-\frac{-\sqrt{601}-19}{12}\right)$$

Evaluate

$$6p^{2}+19p-10$$

Solution Steps

Combine 15p and 4p to get 19p.

$$6p^{2}+19p-10$$