SOLUTION: I have tryed to figure out this equation. The book says it's solving Quadratic Equations by factoring. The answere is (-3,7) The computor says it's not possible to solve, Will you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have tryed to figure out this equation. The book says it's solving Quadratic Equations by factoring. The answere is (-3,7) The computor says it's not possible to solve, Will you      Log On


   

Question 639683: I have tryed to figure out this equation. The book says it's solving Quadratic Equations by factoring. The answere is (-3,7) The computor says it's not possible to solve, Will you show me how to solve it please
x^2-4x=21
Thank you!
Found 2 solutions by reviewermath, MathLover1:
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-21+=+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=%28-4%29%5E2-4%2A1%2A-21=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+7
x%5B2%5D+=+%28-%28-4%29-sqrt%28+100+%29%29%2F2%5C1+=+-3

Quadratic expression 1x%5E2%2B-4x%2B-21 can be factored:
1x%5E2%2B-4x%2B-21+=+1%28x-7%29%2A%28x--3%29
Again, the answer is: 7, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-21+%29

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-4x=21
x%5E2-4x-21=0.........replace -4x with 3x-7x
x%5E2%2B3x-7x-21=0...group first two and second two terms together

%28x%5E2%2B3x%29-%287x%2B21%29=0...factor out x from the first group and 7 from the second group

x%28x%2B3%29-7%28x%2B3%29=0
%28x-7%29%28x%2B3%29=0
now find solutions: recall, product is equal to zero if any of the factors is equal to zero
so, if
%28x-7%29=0....->.....x=7
or
%28x%2B3%29=0..->.....x=-3