Solve 16.8*20h^2+10h

$$16.8 \times 20 h ^ { 2 } + 10 h$$

Factor

$$2h\left(168h+5\right)$$

Steps Using the Quadratic Formula

Multiply 16.8 and 20 to get 336.

$$factor(336h^{2}+10h)$$

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.

$$336h^{2}+10h=0$$

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.

$$h=\frac{-10±\sqrt{10^{2}}}{2\times 336}$$

Take the square root of 10^{2}.

$$h=\frac{-10±10}{2\times 336}$$

Multiply 2 times 336.

$$h=\frac{-10±10}{672}$$

Now solve the equation h=\frac{-10±10}{672} when ± is plus. Add -10 to 10.

$$h=\frac{0}{672}$$

Divide 0 by 672.

$$h=0$$

Now solve the equation h=\frac{-10±10}{672} when ± is minus. Subtract 10 from -10.

$$h=-\frac{20}{672}$$

Reduce the fraction \frac{-20}{672} to lowest terms by extracting and canceling out 4.

$$h=-\frac{5}{168}$$

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{5}{168} for x_{2}.

$$336h^{2}+10h=336h\left(h-\left(-\frac{5}{168}\right)\right)$$

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

$$336h^{2}+10h=336h\left(h+\frac{5}{168}\right)$$

Add \frac{5}{168} to h by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$336h^{2}+10h=336h\times \frac{168h+5}{168}$$

Cancel out 168, the greatest common factor in 336 and 168.

$$336h^{2}+10h=2h\left(168h+5\right)$$

Evaluate

$$2h\left(168h+5\right)$$

Solution Steps

Multiply 16.8 and 20 to get 336.

$$336h^{2}+10h$$