Solve x^2-5x+15=x(x-3)-14+5(x-2)+3113

$$x ^ { 2 } - 5 x + 15 = x ( x - 3 ) - 14 + 5 ( x - 2 ) + 3113$$

Solve for x

$$x = -\frac{3074}{7} = -439\frac{1}{7} \approx -439.142857143$$

Steps for Solving Linear Equation

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

$$x^{2}-5x+15=x^{2}-3x-14+5\left(x-2\right)+3113$$

Use the distributive property to multiply 5 by x-2.

$$x^{2}-5x+15=x^{2}-3x-14+5x-10+3113$$

Combine -3x and 5x to get 2x.

$$x^{2}-5x+15=x^{2}+2x-14-10+3113$$

Subtract 10 from -14 to get -24.

$$x^{2}-5x+15=x^{2}+2x-24+3113$$

Add -24 and 3113 to get 3089.

$$x^{2}-5x+15=x^{2}+2x+3089$$

Subtract x^{2} from both sides.

$$x^{2}-5x+15-x^{2}=2x+3089$$

Combine x^{2} and -x^{2} to get 0.

$$-5x+15=2x+3089$$

Subtract 2x from both sides.

$$-5x+15-2x=3089$$

Combine -5x and -2x to get -7x.

$$-7x+15=3089$$

Subtract 15 from both sides.

$$-7x=3089-15$$

Subtract 15 from 3089 to get 3074.

$$-7x=3074$$

Divide both sides by -7.

$$x=\frac{3074}{-7}$$

Fraction \frac{3074}{-7} can be rewritten as -\frac{3074}{7} by extracting the negative sign.

$$x=-\frac{3074}{7}$$