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

Math
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
Simplify x+7+x+6+x2-2x+3x-3.
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Add x and x.
2x+7+6+x2-2x+3x-3=38
Combine the opposite terms in 2x+7+6+x2-2x+3x-3.
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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.
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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
Factor x2+3x-28 using the AC method.
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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 and solve.
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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 and solve.
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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

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