Solve (1)8x^2+14x

$$( 1 ) 8 x ^ { 2 } + 14 x$$

Factor

$$2x\left(4x+7\right)$$

Solution Steps

Factor out 2.

$$2\left(4x^{2}+7x\right)$$

Consider 4x^{2}+7x. Factor out x.

$$x\left(4x+7\right)$$

Rewrite the complete factored expression.

$$2x\left(4x+7\right)$$

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.

$$8x^{2}+14x=0$$

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.

$$x=\frac{-14±\sqrt{14^{2}}}{2\times 8}$$

Take the square root of 14^{2}.

$$x=\frac{-14±14}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{-14±14}{16}$$

Now solve the equation x=\frac{-14±14}{16} when ± is plus. Add -14 to 14.

$$x=\frac{0}{16}$$

Divide 0 by 16.

$$x=0$$

Now solve the equation x=\frac{-14±14}{16} when ± is minus. Subtract 14 from -14.

$$x=-\frac{28}{16}$$

Reduce the fraction \frac{-28}{16} to lowest terms by extracting and canceling out 4.

$$x=-\frac{7}{4}$$

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{7}{4} for x_{2}.

$$8x^{2}+14x=8x\left(x-\left(-\frac{7}{4}\right)\right)$$

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

$$8x^{2}+14x=8x\left(x+\frac{7}{4}\right)$$

Add \frac{7}{4} to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$8x^{2}+14x=8x\times \frac{4x+7}{4}$$

Cancel out 4, the greatest common factor in 8 and 4.

$$8x^{2}+14x=2x\left(4x+7\right)$$

Evaluate

$$2x\left(4x+7\right)$$

Solution Steps

Multiply 1 and 8 to get 8.

$$8x^{2}+14x$$