Solve 8x+56x^2

$$8x+56 { x }^{ 2 }$$

Factor

$$8x\left(7x+1\right)$$

Solution Steps

Factor out 8.

$$8\left(x+7x^{2}\right)$$

Consider x+7x^{2}. Factor out x.

$$x\left(1+7x\right)$$

Rewrite the complete factored expression.

$$8x\left(7x+1\right)$$

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.

$$56x^{2}+8x=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}}}{2\times 56}$$

Take the square root of 8^{2}.

$$x=\frac{-8±8}{2\times 56}$$

Multiply 2 times 56.

$$x=\frac{-8±8}{112}$$

Now solve the equation x=\frac{-8±8}{112} when ± is plus. Add -8 to 8.

$$x=\frac{0}{112}$$

Divide 0 by 112.

$$x=0$$

Now solve the equation x=\frac{-8±8}{112} when ± is minus. Subtract 8 from -8.

$$x=-\frac{16}{112}$$

Reduce the fraction \frac{-16}{112} to lowest terms by extracting and canceling out 16.

$$x=-\frac{1}{7}$$

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{1}{7} for x_{2}.

$$56x^{2}+8x=56x\left(x-\left(-\frac{1}{7}\right)\right)$$

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

$$56x^{2}+8x=56x\left(x+\frac{1}{7}\right)$$

Add \frac{1}{7} to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$56x^{2}+8x=56x\times \frac{7x+1}{7}$$

Cancel out 7, the greatest common factor in 56 and 7.

$$56x^{2}+8x=8x\left(7x+1\right)$$

Evaluate

$$8x\left(7x+1\right)$$