SOLUTION: please help me solve the following polynomial equation and please show work x^2 - 3x = 10

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Question 90348This question is from textbook algebra and trigonometry
: please help me solve the following polynomial equation and please show work
x^2 - 3x = 10 This question is from textbook algebra and trigonometry

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+3x+=+10

x%5E2+-+3x-+10=0 Subtract 10 from both sides



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

Notice when we graph x%5E2-3%2Ax-10, we get:

+graph%28+500%2C+500%2C+-12%2C+15%2C+-12%2C+15%2C1%2Ax%5E2%2B-3%2Ax%2B-10%29+

and we can see that the roots are x=5 and x=-2. This verifies our answer