Solve 15a^2+93a-216quad25

$$15 a ^ { 2 } + 93 a - 216 \quad 25$$

Factor

$$15\left(a-\frac{-\sqrt{36961}-31}{10}\right)\left(a-\frac{\sqrt{36961}-31}{10}\right)$$

Steps Using the Quadratic Formula

Multiply 216 and 25 to get 5400.

$$factor(15a^{2}+93a-5400)$$

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.

$$15a^{2}+93a-5400=0$$

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.

$$a=\frac{-93±\sqrt{93^{2}-4\times 15\left(-5400\right)}}{2\times 15}$$

Square 93.

$$a=\frac{-93±\sqrt{8649-4\times 15\left(-5400\right)}}{2\times 15}$$

Multiply -4 times 15.

$$a=\frac{-93±\sqrt{8649-60\left(-5400\right)}}{2\times 15}$$

Multiply -60 times -5400.

$$a=\frac{-93±\sqrt{8649+324000}}{2\times 15}$$

Add 8649 to 324000.

$$a=\frac{-93±\sqrt{332649}}{2\times 15}$$

Take the square root of 332649.

$$a=\frac{-93±3\sqrt{36961}}{2\times 15}$$

Multiply 2 times 15.

$$a=\frac{-93±3\sqrt{36961}}{30}$$

Now solve the equation a=\frac{-93±3\sqrt{36961}}{30} when ± is plus. Add -93 to 3\sqrt{36961}.

$$a=\frac{3\sqrt{36961}-93}{30}$$

Divide -93+3\sqrt{36961} by 30.

$$a=\frac{\sqrt{36961}-31}{10}$$

Now solve the equation a=\frac{-93±3\sqrt{36961}}{30} when ± is minus. Subtract 3\sqrt{36961} from -93.

$$a=\frac{-3\sqrt{36961}-93}{30}$$

Divide -93-3\sqrt{36961} by 30.

$$a=\frac{-\sqrt{36961}-31}{10}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-31+\sqrt{36961}}{10} for x_{1} and \frac{-31-\sqrt{36961}}{10} for x_{2}.

$$15a^{2}+93a-5400=15\left(a-\frac{\sqrt{36961}-31}{10}\right)\left(a-\frac{-\sqrt{36961}-31}{10}\right)$$

Evaluate

$$15a^{2}+93a-5400$$

Solution Steps

Multiply 216 and 25 to get 5400.

$$15a^{2}+93a-5400$$