State the quadratic formula and hence solve
x(x + 3) = 6x + 2
Please show your working out, and thank you in
advance for your help
Quadratic formula:
Given Ax² + Bx + C = 0, the solutions are
________
-B ± ÖB² - 4AC
x = —————————————————
2A
x(x + 3) = 6x + 2
x² + 3x = 6x + 2
Get 0 on right by subtracting 6x and 2 from both sides
x² - 3x - 2 = 0
Put 1 in front of x²
1x² - 3x - 2 = 0
Compare that equation to
Ax² + Bx + C = 0
We see that A = 1, B = -3, and C = -2
Substituting in
________
-B ± ÖB² - 4AC
x = —————————————————
2A
________________
-(-1) ± Ö(-1)² - 4(1)(-2)
x = ———————————————————————————
2(1)
_____
1 ± Ö1 + 8
x = ————————————
2
_
1 ± Ö9
x = ————————
2
1 ± 3
x = ————————
2
± means + or -
First solution uses +:
1 + 3 4
x = ——————— = ——— = 2
2 2
Second solution uses -:
1 - 3 -2
x = ——————— = ————— = -1
2 2
Notice that your problem COULD have been solved
simply by factoring:
x(x + 3) = 6x + 2
x² + 3x = 6x + 2
x² - 3x - 2 = 0
(x + 1)(x - 2) = 0
Using 0 factor principle:
x + 1 = 0, so x = -1
x - 2 = 0, so x = 2
However you were told to solve it by the
quadratic formula to get practice because
most quadratic equations can't be solved
by factoring.
Edwin
AnlytcPhil@aol.com
