SOLUTION: Solve by using the quadratic formula. 5x^2 + x = 3

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Question 89362: Solve by using the quadratic formula.
5x^2 + x = 3
Found 2 solutions by jim_thompson5910, malakumar_kos@yahoo.com:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5x%5E2+%2B+x+=+3

5x%5E2+%2B+x+-+3=0 Subtract 3 from both sides

Now 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 5%2Ax%5E2%2Bx-3=0 ( notice a=5, b=1, and c=-3)

x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A5%2A-3+%29%29%2F%282%2A5%29 Plug in a=5, b=1, and c=-3



x+=+%28-1+%2B-+sqrt%28+1-4%2A5%2A-3+%29%29%2F%282%2A5%29 Square 1 to get 1



x+=+%28-1+%2B-+sqrt%28+1%2B60+%29%29%2F%282%2A5%29 Multiply -4%2A-3%2A5 to get 60



x+=+%28-1+%2B-+sqrt%28+61+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-1+%2B-+sqrt%2861%29%29%2F%282%2A5%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-1+%2B-+sqrt%2861%29%29%2F10 Multiply 2 and 5 to get 10

So now the expression breaks down into two parts

x+=+%28-1+%2B+sqrt%2861%29%29%2F10 or x+=+%28-1+-+sqrt%2861%29%29%2F10


Now break up the fraction


x=-1%2F10%2Bsqrt%2861%29%2F10 or x=-1%2F10-sqrt%2861%29%2F10



So these expressions approximate to

x=0.681024967590665 or x=-0.881024967590665


So our solutions are:
x=0.681024967590665 or x=-0.881024967590665

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



when we use the root finder feature on a calculator, we find that x=0.681024967590665 and x=-0.881024967590665.So this verifies our answer

Answer by malakumar_kos@yahoo.com(315) About Me  (Show Source):
You can put this solution on YOUR website!

Solve by using the quadratic formula.
5x^2 + x = 3
5x^2+x-3 = 0 compare with the std form ax^2+bx+c= 0
we get a= 5, b = 1 and c= -3
the std formula is x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2%2Aa%2A
x = (-1+-sqrt(1^2-4*5*-3)/2*5
= {-1+-sqrt(1+60)}/10
= {-1+-sqrt(61)}/10