SOLUTION: 9) Solve by using quadratic formula x2 + 2x – 4 = 0

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Question 294772: 9) Solve by using quadratic formula x2 + 2x – 4 = 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!
9)

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2%2B2%2Ax-4=0 ( notice a=1, b=2, and c=-4)





x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29 Plug in a=1, b=2, and c=-4




x+=+%28-2+%2B-+sqrt%28+4-4%2A1%2A-4+%29%29%2F%282%2A1%29 Square 2 to get 4




x+=+%28-2+%2B-+sqrt%28+4%2B16+%29%29%2F%282%2A1%29 Multiply -4%2A-4%2A1 to get 16




x+=+%28-2+%2B-+sqrt%28+20+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-2+%2B-+2%2Asqrt%285%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-2+%2B-+2%2Asqrt%285%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-2+%2B+2%2Asqrt%285%29%29%2F2 or x+=+%28-2+-+2%2Asqrt%285%29%29%2F2



Now break up the fraction



x=-2%2F2%2B2%2Asqrt%285%29%2F2 or x=-2%2F2-2%2Asqrt%285%29%2F2



Simplify



x=-1%2Bsqrt%285%29 or x=-1-sqrt%285%29



So the solutions are:

x=-1%2Bsqrt%285%29 or x=-1-sqrt%285%29





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10)

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-3%2Ax-10=0 ( notice a=1, b=-3, and c=-10)





x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A-10+%29%29%2F%282%2A1%29 Plug in a=1, b=-3, and c=-10




x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A-10+%29%29%2F%282%2A1%29 Negate -3 to get 3




x+=+%283+%2B-+sqrt%28+9-4%2A1%2A-10+%29%29%2F%282%2A1%29 Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because %28-3%29%5E2=-3%2A-3=9.)




x+=+%283+%2B-+sqrt%28+9%2B40+%29%29%2F%282%2A1%29 Multiply -4%2A-10%2A1 to get 40




x+=+%283+%2B-+sqrt%28+49+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%283+%2B-+7%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%283+%2B-+7%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%283+%2B+7%29%2F2 or x+=+%283+-+7%29%2F2


Lets look at the first part:


x=%283+%2B+7%29%2F2


x=10%2F2 Add the terms in the numerator

x=5 Divide


So one answer is

x=5




Now lets look at the second part:


x=%283+-+7%29%2F2


x=-4%2F2 Subtract the terms in the numerator

x=-2 Divide


So another answer is

x=-2


So our solutions are:

x=5 or x=-2

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Do not submit more than one problem at a time
No similar problems and
Limit of 4 problems daily (daily not at a time)
So you used up your quota for the day in one submission.
x^2 is x^2 not x2 which can be understand as 2x