SOLUTION: Multiply and simplify your answer (w+1/5)(w+1/4) Find the x intercept for the graph of the equation. y+x^2-3x-10

Algebra ->  Rational-functions -> SOLUTION: Multiply and simplify your answer (w+1/5)(w+1/4) Find the x intercept for the graph of the equation. y+x^2-3x-10       Log On


   

Question 473335: Multiply and simplify your answer
(w+1/5)(w+1/4)
Find the x intercept for the graph of the equation.
y+x^2-3x-10

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%28w%2B1%2F5%29%28w%2B1%2F4%29
w%5E2%2B%281%2F5%29w%2B%281%2F4%29w%2B%281%2F5%29%281%2F4%29

=w%5E2%2B%281%2A4%2F5%2A4%29w%2B%281%2A5%2F4%2A5%29w%2B%281%2F20%29

=w%5E2%2B%284%2F20%29w%2B%285%2F20%29w%2B%281%2F20%29

=w%5E2%2B%289%2F20%29w%2B%281%2F20%29
=20w%5E2%2B9w%2B1

Find the x-+intercept for the graph of the equation.
I guess you have:
y=x%5E2-3x-10.....set y=0 and solve for x
0%2Bx%5E2-3x-10
x%5E2-3x-10=0.....use quadratic formula
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




+graph%28+500%2C+500%2C+-15%2C10%2C+-15%2C+10%2C+x%5E2-3x-10%29+