Solve 9x+16x^2

$$9x+16 { x }^{ 2 }$$

Factor

$$x\left(16x+9\right)$$

Solution Steps

Factor out x.

$$x\left(9+16x\right)$$

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.

$$16x^{2}+9x=0$$

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.

$$x=\frac{-9±\sqrt{9^{2}}}{2\times 16}$$

Take the square root of 9^{2}.

$$x=\frac{-9±9}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{-9±9}{32}$$

Now solve the equation x=\frac{-9±9}{32} when ± is plus. Add -9 to 9.

$$x=\frac{0}{32}$$

Divide 0 by 32.

$$x=0$$

Now solve the equation x=\frac{-9±9}{32} when ± is minus. Subtract 9 from -9.

$$x=-\frac{18}{32}$$

Reduce the fraction \frac{-18}{32} to lowest terms by extracting and canceling out 2.

$$x=-\frac{9}{16}$$

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 -\frac{9}{16} for x_{2}.

$$16x^{2}+9x=16x\left(x-\left(-\frac{9}{16}\right)\right)$$

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

$$16x^{2}+9x=16x\left(x+\frac{9}{16}\right)$$

Add \frac{9}{16} to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$16x^{2}+9x=16x\times \frac{16x+9}{16}$$

Cancel out 16, the greatest common factor in 16 and 16.

$$16x^{2}+9x=x\left(16x+9\right)$$

Evaluate

$$x\left(16x+9\right)$$