Solve m-61m^2-11m+30

$$m - 61 m ^ { 2 } - 11 m + 30$$

Factor

$$-61\left(m-\frac{-\sqrt{1855}-5}{61}\right)\left(m-\frac{\sqrt{1855}-5}{61}\right)$$

Steps Using the Quadratic Formula

Combine m and -11m to get -10m.

$$factor(-10m-61m^{2}+30)$$

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.

$$-61m^{2}-10m+30=0$$

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.

$$m=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\left(-61\right)\times 30}}{2\left(-61\right)}$$

Square -10.

$$m=\frac{-\left(-10\right)±\sqrt{100-4\left(-61\right)\times 30}}{2\left(-61\right)}$$

Multiply -4 times -61.

$$m=\frac{-\left(-10\right)±\sqrt{100+244\times 30}}{2\left(-61\right)}$$

Multiply 244 times 30.

$$m=\frac{-\left(-10\right)±\sqrt{100+7320}}{2\left(-61\right)}$$

Add 100 to 7320.

$$m=\frac{-\left(-10\right)±\sqrt{7420}}{2\left(-61\right)}$$

Take the square root of 7420.

$$m=\frac{-\left(-10\right)±2\sqrt{1855}}{2\left(-61\right)}$$

The opposite of -10 is 10.

$$m=\frac{10±2\sqrt{1855}}{2\left(-61\right)}$$

Multiply 2 times -61.

$$m=\frac{10±2\sqrt{1855}}{-122}$$

Now solve the equation m=\frac{10±2\sqrt{1855}}{-122} when ± is plus. Add 10 to 2\sqrt{1855}.

$$m=\frac{2\sqrt{1855}+10}{-122}$$

Divide 10+2\sqrt{1855} by -122.

$$m=\frac{-\sqrt{1855}-5}{61}$$

Now solve the equation m=\frac{10±2\sqrt{1855}}{-122} when ± is minus. Subtract 2\sqrt{1855} from 10.

$$m=\frac{10-2\sqrt{1855}}{-122}$$

Divide 10-2\sqrt{1855} by -122.

$$m=\frac{\sqrt{1855}-5}{61}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-5-\sqrt{1855}}{61} for x_{1} and \frac{-5+\sqrt{1855}}{61} for x_{2}.

$$-61m^{2}-10m+30=-61\left(m-\frac{-\sqrt{1855}-5}{61}\right)\left(m-\frac{\sqrt{1855}-5}{61}\right)$$

Evaluate

$$30-10m-61m^{2}$$

Solution Steps

Combine m and -11m to get -10m.

$$-10m-61m^{2}+30$$