Michael J. answered • 06/09/15
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Effective High School STEM Tutor & CUNY Math Peer Leader
A quadratic equation is always in the form
ax2 + bx + c = 0
where:
a, b, and c are constants.
The quadratic formula is
x = (-b ± √(b2 - 4ac)) / 2a
The plus/minus sign indicates that you will have two solutions.
From the first part of the problem, if we subtract 14x on both sides of equation, we obtain
5x2 - 14x - 3 = 0
a = 5
b = -14
c = -3
From the second part of the problem, if we subtract x and subtract 1/6 on both sides of equation, we obtain.
(1/3)x2 - x - (1/6) = 0
a = 1/3
b = -1
c = -1/6
Plug in the values of a, b, and c into the formula for each equation respectively to obtain your solutions.
Andrew M.
on the 2nd problem:
We can actually use 6 instead of 18 to eliminate the fraction... the smaller numbers would be obtained by multiplying the original equation through by 6 giving 2x2-6x-1
This gives a = 2, b = -6, c = -1
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Also, David... you accidentally switched the sign of the constant... your equation should be
6x2 -18x - 3
I just reduced it again by dividing out the 3 as a common factor of that
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06/10/15
David W.
06/09/15