SOLUTION: The square of a number plus the number is 132. What is the number?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: The square of a number plus the number is 132. What is the number?      Log On


   

Question 255371: The square of a number plus the number is 132. What is the number?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since "The square of a number plus the number is 132", we know that x%5E2%2Bx=132




x%5E2%2Bx=132 Start with the given equation.


x%5E2%2Bx-132=0 Subtract 132 from both sides.


Notice that the quadratic x%5E2%2Bx-132 is in the form of Ax%5E2%2BBx%2BC where A=1, B=1, and C=-132


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%281%29+%2B-+sqrt%28+%281%29%5E2-4%281%29%28-132%29+%29%29%2F%282%281%29%29 Plug in A=1, B=1, and C=-132


x+=+%28-1+%2B-+sqrt%28+1-4%281%29%28-132%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--528+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-132%29 to get -528


x+=+%28-1+%2B-+sqrt%28+1%2B528+%29%29%2F%282%281%29%29 Rewrite sqrt%281--528%29 as sqrt%281%2B528%29


x+=+%28-1+%2B-+sqrt%28+529+%29%29%2F%282%281%29%29 Add 1 to 528 to get 529


x+=+%28-1+%2B-+sqrt%28+529+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-1+%2B-+23%29%2F%282%29 Take the square root of 529 to get 23.


x+=+%28-1+%2B+23%29%2F%282%29 or x+=+%28-1+-+23%29%2F%282%29 Break up the expression.


x+=+%2822%29%2F%282%29 or x+=++%28-24%29%2F%282%29 Combine like terms.


x+=+11 or x+=+-12 Simplify.


So the solutions are x+=+11 or x+=+-12 which means that the number is either 11 or -12