38=x+7+x+6+x2-2x+3x-3

Rewrite the equation as x+7+x+6+x2-2x+3x-3=38.

x+7+x+6+x2-2x+3x-3=38

Add x and x.

2x+7+6+x2-2x+3x-3=38

Combine the opposite terms in 2x+7+6+x2-2x+3x-3.

Subtract 2x from 2x.

7+6+x2+0+3x-3=38

Add 7+6+x2 and 0.

7+6+x2+3x-3=38

7+6+x2+3x-3=38

Simplify by adding and subtracting.

Add 7 and 6.

13+x2+3x-3=38

Subtract 3 from 13.

x2+3x+10=38

x2+3x+10=38

x2+3x+10=38

Move 38 to the left side of the equation by subtracting it from both sides.

x2+3x+10-38=0

Subtract 38 from 10.

x2+3x-28=0

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -28 and whose sum is 3.

-4,7

Write the factored form using these integers.

(x-4)(x+7)=0

(x-4)(x+7)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x-4=0

x+7=0

Set the first factor equal to 0.

x-4=0

Add 4 to both sides of the equation.

x=4

x=4

Set the next factor equal to 0.

x+7=0

Subtract 7 from both sides of the equation.

x=-7

x=-7

The final solution is all the values that make (x-4)(x+7)=0 true.

x=4,-7

Solve using the Square Root Property 38=x+7+x+6+x^2-2x+3x-3