SOLUTION: If the square of a number increased by the number is 42, then what is the number? I have x^2+x=42, but I do not know if this is correct and if so, what to do after that

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: If the square of a number increased by the number is 42, then what is the number? I have x^2+x=42, but I do not know if this is correct and if so, what to do after that      Log On


   

Question 630090: If the square of a number increased by the number is 42, then what is the number?
I have x^2+x=42, but I do not know if this is correct and if so, what to do after that
Found 3 solutions by Alan3354, graphmatics, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If the square of a number increased by the number is 42, then what is the number?
I have x^2+x=42, but I do not know if this is correct and if so, what to do after that
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x%5E2%2Bx=42
x%5E2%2Bx-42+=+0
(x+7)*(x-6) = 0
x = -7, or x = 6

Answer by graphmatics(170) About Me  (Show Source):
You can put this solution on YOUR website!
Your equation +x%5E2%2Bx=42+ is correct. Simply move the 42 to the left side of the equation as -42 to get +x%5E2%2Bx-42=0+. Now apply the quadratic equation.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-42+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%281%29%5E2-4%2A1%2A-42=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+169+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%281%29-sqrt%28+169+%29%29%2F2%5C1+=+-7

Quadratic expression 1x%5E2%2B1x%2B-42 can be factored:
1x%5E2%2B1x%2B-42+=+1%28x-6%29%2A%28x--7%29
Again, the answer is: 6, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-42+%29
6 is the solution.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
That is correct
+x+%5E2+%2B+x+=+42+
complete the square
Take 1/2 of the coefficient of
+x+, square it, and add it
to both sides
+x%5E2+%2B+x+%2B+%281%2F2%29%5E2+=+42+%2B+%281%2F2%29%5E2+
+x%5E2+%2B+x+%2B+1%2F4+=+42+%2B+1%2F4+
+x%5E2+%2B+x+%2B+1%2F4+=+168%2F4+%2B+1%2F4+
+x%5E2+%2B+x+%2B+1%2F4+=+169%2F4+
+%28+x+%2B+1%2F2+%29%5E2+=+%2813%2F2%29%5E2+
Take the square root of both sides
+x+%2B+1%2F2+=+13%2F2+
+x+=+12%2F2+
+x+=+6+
The number is 6
check:
+x+%5E2+%2B+x+=+42+
+6+%5E2+%2B+6+=+42+
+36+%2B+6+=+42+
+42+=+42+
OK