SOLUTION: Use the quadratic formula to solve the equation x^2-3x=7 The solution set is _?_ (type one exact answer, using radicals as needed.Express complex numbers in terms of i u

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Question 346176: Use the quadratic formula to solve the equation
x^2-3x=7
The solution set is _?_
(type one exact answer, using radicals as needed.Express complex numbers in terms of i use integers or fractions for any numbers in the expressio. use a comma to seperate answers as needed.)
Thank you
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
In answer to Your Question:
Solution Set would be the values found for x%5B1%5D , x%5B2%5D
x%5E2-3x=7
Written as an Quadratic Equation:
x%5E2-3x-7=0
.
Using the Quadratic Formula to Solve:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-3x%2B-7+=+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=%28-3%29%5E2-4%2A1%2A-7=37.

Discriminant d=37 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+37+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+37+%29%29%2F2%5C1+=+4.54138126514911
x%5B2%5D+=+%28-%28-3%29-sqrt%28+37+%29%29%2F2%5C1+=+-1.54138126514911

Quadratic expression 1x%5E2%2B-3x%2B-7 can be factored:
1x%5E2%2B-3x%2B-7+=+1%28x-4.54138126514911%29%2A%28x--1.54138126514911%29
Again, the answer is: 4.54138126514911, -1.54138126514911. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-7+%29