Solve h(x)=-32x^2/(45)^2+x+200

$$h ( x ) = \frac { - 32 x ^ { 2 } } { ( 45 ) ^ { 2 } } + x + 200$$

Evaluate

$$-\frac{32x^{2}}{2025}+x+200$$

Short Solution Steps

Calculate 45 to the power of 2 and get 2025.

$$\frac{-32x^{2}}{2025}+x+200$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x+200 times \frac{2025}{2025}.

$$\frac{-32x^{2}}{2025}+\frac{2025\left(x+200\right)}{2025}$$

Since \frac{-32x^{2}}{2025} and \frac{2025\left(x+200\right)}{2025} have the same denominator, add them by adding their numerators.

$$\frac{-32x^{2}+2025\left(x+200\right)}{2025}$$

Do the multiplications in -32x^{2}+2025\left(x+200\right).

$$\frac{-32x^{2}+2025x+405000}{2025}$$

Factor

$$-\frac{32}{2025}\left(x-\frac{2025-225\sqrt{1105}}{64}\right)\left(x-\frac{225\sqrt{1105}+2025}{64}\right)$$