If `x ^(2) -7x =30 and x gt0,` what is the value of `x -5` ?

Options

A. 5
B. 6
C. 10
D. 25

Answer

A

Explanation

Set the equation equal to zero and factor the first term:
`x ^(2) -7x=30`
`x ^(2) -7x -30=0`
`( x pm ?) (x pm ?) =0`
Next, consider factors of -30, keeping in mind that they must sum to -7, so the facotr with the greater absolute volue must be negative. The possibilities are: `-30xx1, -15 xx2, -10xx3, and -6 xx5.` The factor pair that sums to -7 is `-10 xx 3.` Write that factor pair into your binomials:
` (x-10) (x+3)=0`
Set each factor equal to zero and solve:
`(x -10) =0 " "(x+3)=0`
`x =10 " "x =-3`
The question says that `x gt0, so x =10.` Now that you solved for x, you can answer the question, which asks for `x -5:10-5=5.` (A) is correct.