Solve 1.0986+0.2877(x-3)+(-0.0323)(x-3)(x-4)

$$1.0986 + 0.2877 ( x - 3 ) + ( - 0.0323 ) ( x - 3 ) ( x - 4 )$$

Evaluate

$$-\frac{323x^{2}}{10000}+\frac{2569x}{5000}-0.1521$$

Solution Steps

Use the distributive property to multiply 0.2877 by x-3.

$$1.0986+0.2877x-0.8631-0.0323\left(x-3\right)\left(x-4\right)$$

Subtract 0.8631 from 1.0986 to get 0.2355.

$$0.2355+0.2877x-0.0323\left(x-3\right)\left(x-4\right)$$

Use the distributive property to multiply -0.0323 by x-3.

$$0.2355+0.2877x+\left(-0.0323x+0.0969\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of -0.0323x+0.0969 by each term of x-4.

$$0.2355+0.2877x-0.0323x^{2}+0.1292x+0.0969x-0.3876$$

Combine 0.1292x and 0.0969x to get 0.2261x.

$$0.2355+0.2877x-0.0323x^{2}+0.2261x-0.3876$$

Combine 0.2877x and 0.2261x to get 0.5138x.

$$0.2355+0.5138x-0.0323x^{2}-0.3876$$

Subtract 0.3876 from 0.2355 to get -0.1521.

$$-0.1521+0.5138x-0.0323x^{2}$$

Expand

$$-\frac{323x^{2}}{10000}+\frac{2569x}{5000}-0.1521$$

Solution Steps

Use the distributive property to multiply 0.2877 by x-3.

$$1.0986+0.2877x-0.8631-0.0323\left(x-3\right)\left(x-4\right)$$

Subtract 0.8631 from 1.0986 to get 0.2355.

$$0.2355+0.2877x-0.0323\left(x-3\right)\left(x-4\right)$$

Use the distributive property to multiply -0.0323 by x-3.

$$0.2355+0.2877x+\left(-0.0323x+0.0969\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of -0.0323x+0.0969 by each term of x-4.

$$0.2355+0.2877x-0.0323x^{2}+0.1292x+0.0969x-0.3876$$

Combine 0.1292x and 0.0969x to get 0.2261x.

$$0.2355+0.2877x-0.0323x^{2}+0.2261x-0.3876$$

Combine 0.2877x and 0.2261x to get 0.5138x.

$$0.2355+0.5138x-0.0323x^{2}-0.3876$$

Subtract 0.3876 from 0.2355 to get -0.1521.

$$-0.1521+0.5138x-0.0323x^{2}$$