Solve 1/2*9.81*x-1/2*9.81*left(x-0.85right)^2

$$\frac{ 1 }{ 2 } \times 9.81 \times x- \frac{ 1 }{ 2 } \times 9.81 \times { \left(x-0.85 \right) }^{ 2 }$$

Evaluate

$$\frac{981\left(-\left(x-0.85\right)^{2}+x\right)}{200}$$

Solution Steps

Multiply \frac{1}{2} and 9.81 to get \frac{981}{200}.

$$\frac{981}{200}x-\frac{1}{2}\times 9.81\left(x-0.85\right)^{2}$$

Multiply \frac{1}{2} and 9.81 to get \frac{981}{200}.

$$\frac{981}{200}x-\frac{981}{200}\left(x-0.85\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-0.85\right)^{2}.

$$\frac{981}{200}x-\frac{981}{200}\left(x^{2}-1.7x+0.7225\right)$$

Use the distributive property to multiply -\frac{981}{200} by x^{2}-1.7x+0.7225.

$$\frac{981}{200}x-\frac{981}{200}x^{2}+\frac{16677}{2000}x-\frac{283509}{80000}$$

Combine \frac{981}{200}x and \frac{16677}{2000}x to get \frac{26487}{2000}x.

$$\frac{26487}{2000}x-\frac{981}{200}x^{2}-\frac{283509}{80000}$$

Expand

$$-\frac{981x^{2}}{200}+\frac{26487x}{2000}-3.5438625$$

Solution Steps

Multiply \frac{1}{2} and 9.81 to get \frac{981}{200}.

$$\frac{981}{200}x-\frac{1}{2}\times 9.81\left(x-0.85\right)^{2}$$

Multiply \frac{1}{2} and 9.81 to get \frac{981}{200}.

$$\frac{981}{200}x-\frac{981}{200}\left(x-0.85\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-0.85\right)^{2}.

$$\frac{981}{200}x-\frac{981}{200}\left(x^{2}-1.7x+0.7225\right)$$

Use the distributive property to multiply -\frac{981}{200} by x^{2}-1.7x+0.7225.

$$\frac{981}{200}x-\frac{981}{200}x^{2}+\frac{16677}{2000}x-\frac{283509}{80000}$$

Combine \frac{981}{200}x and \frac{16677}{2000}x to get \frac{26487}{2000}x.

$$\frac{26487}{2000}x-\frac{981}{200}x^{2}-\frac{283509}{80000}$$