SOLUTION: Solve by using quadratic formula x2 – 3x - 10 = 0

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Question 280209: Solve by using quadratic formula x2 – 3x - 10 = 0
Found 2 solutions by jim_thompson5910, richwmiller:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-3x-10=0 Start with the given equation.


Notice that the quadratic x%5E2-3x-10 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-3, and C=-10


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-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-10%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-3, and C=-10


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-10%29+%29%29%2F%282%281%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%281%29%28-10%29+%29%29%2F%282%281%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9--40+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-10%29 to get -40


x+=+%283+%2B-+sqrt%28+9%2B40+%29%29%2F%282%281%29%29 Rewrite sqrt%289--40%29 as sqrt%289%2B40%29


x+=+%283+%2B-+sqrt%28+49+%29%29%2F%282%281%29%29 Add 9 to 40 to get 49


x+=+%283+%2B-+sqrt%28+49+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%283+%2B-+7%29%2F%282%29 Take the square root of 49 to get 7.


x+=+%283+%2B+7%29%2F%282%29 or x+=+%283+-+7%29%2F%282%29 Break up the expression.


x+=+%2810%29%2F%282%29 or x+=++%28-4%29%2F%282%29 Combine like terms.


x+=+5 or x+=+-2 Simplify.


So the solutions are x+=+5 or x+=+-2


Answer by richwmiller(17219) 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-3x%2B-10+=+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-10=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+49+%29%29%2F2%5C1+=+5
x%5B2%5D+=+%28-%28-3%29-sqrt%28+49+%29%29%2F2%5C1+=+-2

Quadratic expression 1x%5E2%2B-3x%2B-10 can be factored:
1x%5E2%2B-3x%2B-10+=+1%28x-5%29%2A%28x--2%29
Again, the answer is: 5, -2. 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-10+%29