Solve -1/4x^2+17+1/5x(-3/25x+25)+1/7x(-frac{1}{35}x+20)

$$- \frac { 1 } { 4 } x ^ { 2 } + 17 + \frac { 1 } { 5 } x ( - \frac { 3 } { 25 } x + 25 ) + \frac { 1 } { 7 } x ( - \frac { 1 } { 35 } x + 20 )$$

Evaluate

$$-\frac{6813x^{2}}{24500}+\frac{55x}{7}+17$$

Solution Steps

Use the distributive property to multiply \frac{1}{5}x by -\frac{3}{25}x+25.

$$-\frac{1}{4}x^{2}+17-\frac{3}{125}x^{2}+5x+\frac{1}{7}x\left(-\frac{1}{35}x+20\right)$$

Combine -\frac{1}{4}x^{2} and -\frac{3}{125}x^{2} to get -\frac{137}{500}x^{2}.

$$-\frac{137}{500}x^{2}+17+5x+\frac{1}{7}x\left(-\frac{1}{35}x+20\right)$$

Use the distributive property to multiply \frac{1}{7}x by -\frac{1}{35}x+20.

$$-\frac{137}{500}x^{2}+17+5x-\frac{1}{245}x^{2}+\frac{20}{7}x$$

Combine -\frac{137}{500}x^{2} and -\frac{1}{245}x^{2} to get -\frac{6813}{24500}x^{2}.

$$-\frac{6813}{24500}x^{2}+17+5x+\frac{20}{7}x$$

Combine 5x and \frac{20}{7}x to get \frac{55}{7}x.

$$-\frac{6813}{24500}x^{2}+17+\frac{55}{7}x$$

Expand

$$-\frac{6813x^{2}}{24500}+\frac{55x}{7}+17$$

Solution Steps

Use the distributive property to multiply \frac{1}{5}x by -\frac{3}{25}x+25.

$$-\frac{1}{4}x^{2}+17-\frac{3}{125}x^{2}+5x+\frac{1}{7}x\left(-\frac{1}{35}x+20\right)$$

Combine -\frac{1}{4}x^{2} and -\frac{3}{125}x^{2} to get -\frac{137}{500}x^{2}.

$$-\frac{137}{500}x^{2}+17+5x+\frac{1}{7}x\left(-\frac{1}{35}x+20\right)$$

Use the distributive property to multiply \frac{1}{7}x by -\frac{1}{35}x+20.

$$-\frac{137}{500}x^{2}+17+5x-\frac{1}{245}x^{2}+\frac{20}{7}x$$

Combine -\frac{137}{500}x^{2} and -\frac{1}{245}x^{2} to get -\frac{6813}{24500}x^{2}.

$$-\frac{6813}{24500}x^{2}+17+5x+\frac{20}{7}x$$

Combine 5x and \frac{20}{7}x to get \frac{55}{7}x.

$$-\frac{6813}{24500}x^{2}+17+\frac{55}{7}x$$