The number is either -11 or 12
Step-by-step explanation:
Let x be the number
Then
According to:
"if a number is subtracted from its square, the result is 132"
[tex]x^2-x = 132\\x^2-x-132 = 0[/tex]
Making factors of 132 that add up to -1
[tex]x^2-12x+11x-132 = 0\\x(x-12)+11(x-12) = 0\\(x-12)(x+11) = 0\\x-12 = 0 => x = 12\\x+11 = 0 => x=-11[/tex]
Putting x=-11 in
[tex]x^2-x = 132\\(-11)^2-(-11) = 132\\121+11 = 132\\132 = 132[/tex]
Putting x = 12
[tex]x^2-x = 132\\(12)^2 - 12 = 132\\144-12 = 132\\132 = 132[/tex]
Hence,
The number is either -11 or 12
Keywords: factorization, variables
Learn more about factorization at:
- brainly.com/question/4695279
- brainly.com/question/4703807
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