Solve 9^3-6g^2-6g

$$9 ^ { 3 } - 6 g ^ { 2 } - 6 g$$

Factor

$$-6\left(g-\frac{-\sqrt{487}-1}{2}\right)\left(g-\frac{\sqrt{487}-1}{2}\right)$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 3 and get 729.

$$factor(729-6g^{2}-6g)$$

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.

$$-6g^{2}-6g+729=0$$

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.

$$g=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-6\right)\times 729}}{2\left(-6\right)}$$

Square -6.

$$g=\frac{-\left(-6\right)±\sqrt{36-4\left(-6\right)\times 729}}{2\left(-6\right)}$$

Multiply -4 times -6.

$$g=\frac{-\left(-6\right)±\sqrt{36+24\times 729}}{2\left(-6\right)}$$

Multiply 24 times 729.

$$g=\frac{-\left(-6\right)±\sqrt{36+17496}}{2\left(-6\right)}$$

Add 36 to 17496.

$$g=\frac{-\left(-6\right)±\sqrt{17532}}{2\left(-6\right)}$$

Take the square root of 17532.

$$g=\frac{-\left(-6\right)±6\sqrt{487}}{2\left(-6\right)}$$

The opposite of -6 is 6.

$$g=\frac{6±6\sqrt{487}}{2\left(-6\right)}$$

Multiply 2 times -6.

$$g=\frac{6±6\sqrt{487}}{-12}$$

Now solve the equation g=\frac{6±6\sqrt{487}}{-12} when ± is plus. Add 6 to 6\sqrt{487}.

$$g=\frac{6\sqrt{487}+6}{-12}$$

Divide 6+6\sqrt{487} by -12.

$$g=\frac{-\sqrt{487}-1}{2}$$

Now solve the equation g=\frac{6±6\sqrt{487}}{-12} when ± is minus. Subtract 6\sqrt{487} from 6.

$$g=\frac{6-6\sqrt{487}}{-12}$$

Divide 6-6\sqrt{487} by -12.

$$g=\frac{\sqrt{487}-1}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-1-\sqrt{487}}{2} for x_{1} and \frac{-1+\sqrt{487}}{2} for x_{2}.

$$-6g^{2}-6g+729=-6\left(g-\frac{-\sqrt{487}-1}{2}\right)\left(g-\frac{\sqrt{487}-1}{2}\right)$$

Evaluate

$$729-6g-6g^{2}$$

Solution Steps

Calculate 9 to the power of 3 and get 729.

$$729-6g^{2}-6g$$