SOLUTION: factor completely: x^2+9x=8

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Start with the given equation

Subtract 8 from both sides


Now let's factor

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)

In order to factor , first multiply the leading coefficient 1 and the last term -8 to get -8. Now we need to ask ourselves: What two numbers multiply to -8 and add to 9? Lets find out by listing all of the possible factors of -8 Factors: 1,2,4,8, -1,-2,-4,-8, List the negative factors as well. This will allow us to find all possible combinations These factors pair up to multiply to -8. (-1)*(8)=-8 (-2)*(4)=-8 Now which of these pairs add to 9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 9 |||| First Number | Second Number | Sum 1 | -8 | 1+(-8)=-7 2 | -4 | 2+(-4)=-2 -1 | 8 | (-1)+8=7 -2 | 4 | (-2)+4=2 None of these factors add to 9. So the quadratic cannot be factored.