Solve 27x^2+243x

$$27 { x }^{ 2 } +243x$$

Factor

$$27x\left(x+9\right)$$

Solution Steps

Factor out 27.

$$27\left(x^{2}+9x\right)$$

Consider x^{2}+9x. Factor out x.

$$x\left(x+9\right)$$

Rewrite the complete factored expression.

$$27x\left(x+9\right)$$

Steps Using the Quadratic Formula

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.

$$27x^{2}+243x=0$$

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.

$$x=\frac{-243±\sqrt{243^{2}}}{2\times 27}$$

Take the square root of 243^{2}.

$$x=\frac{-243±243}{2\times 27}$$

Multiply 2 times 27.

$$x=\frac{-243±243}{54}$$

Now solve the equation x=\frac{-243±243}{54} when ± is plus. Add -243 to 243.

$$x=\frac{0}{54}$$

Divide 0 by 54.

$$x=0$$

Now solve the equation x=\frac{-243±243}{54} when ± is minus. Subtract 243 from -243.

$$x=-\frac{486}{54}$$

Divide -486 by 54.

$$x=-9$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -9 for x_{2}.

$$27x^{2}+243x=27x\left(x-\left(-9\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$27x^{2}+243x=27x\left(x+9\right)$$

Evaluate

$$27x\left(x+9\right)$$