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@third-meow
Last active May 10, 2020 06:43
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## Quadratics Review
Solve for x:
x^2 - 11x - 26 = 0
(x - 13)(x + 2) = 0
x^2 + 8x - 20 = 0
(x - 2)(x + 10) = 0
x^2 + 4x - 21 = 0
(x + 7)(x - 3) = 0
x^2 + x - 2 = 0
(x + 2)(x - 1) = 0
x^2 + 13x + 40 = 0
(x + 8)(x + 5) = 0
x^2 + 2x - 99 = 0
(x - 9)(x + 11) = 0
x^2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)^2 = 0
x^2 - 14x + 24 = 0
(x - 12)(x - 2) = 0
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Solve for x:
ax^2 + bx + c = 0
-b +/- sqrt(b^2 - 4ac)
----------------------
2a
3x^2 + 15x + 18 = 0
(3x + 9)(x + 2) = 0
6x^2 - 5x - 4 = 0
5 +/- sqrt(121)
------------------------
12
5 +/- 11
--------
12
roots = 1.333 , -0.5
16x^2 + 0x - 49 = 0
(4x + 7)(4x - 7) = 0
12x^2 + 17x - 5 = 0
-17 +/- 23
----------------------------
24
roots = 0.25 and -40/24
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Solve for x:
24x^2 - 18x + 0 = 0
4x^2 - 3x = 0
x(4x - 3) = 0
2 - 8x^2 = 0
8x^2 + 0x - 2 = 0
4x^2 - 1 = 0
(2x + 1)(2x - 1) = 0
3x^2 - 27 = 0
(x + 3)(x - 3) = 0
x^2 - 6x + 2 = 0
sqrt(a)/sqrt(b) = sqrt(a/b)
6 +/- sqrt(28)
---------------------
sqrt(4)
3 +/- sqrt(7)
roots = (3 + sqrt(7)), (3 - sqrt(7))
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Solve:
52k + 12 = 9k^2
0 = 9k^2 - 52k - 12
0 = (9k + 2)(k - 6)
k = 6
k = -2/9
3h^2 - 4h - 15 = 0
4 +/- 14
-------------------
6
roots = 18/6 = 3
= -10/6
x^2 - 2ax + a^2 = 0
2a +/- sqrt(4a^2 - 4a^2)
-------------------------
2
roots = a
x^2 - 4ax + 3a^2 = 0
4a +/- 2a
-------------------
2
roots = 3a, a :)
x^2 - 4a^2 = 0
0 +/- 4a
-----------
2
roots = 2a, -2a
x^2 + ax - 2a^2 = 0
a +/- 3a
---------------------
2
roots 2a, -a :))
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Surds Reminder:
(4 + sqrt(5)) (3 + sqrt(2)) 12 + 4sqrt(2) + 3sqrt(5) + sqrt(10)
------------- * -------------- = ------------------------------------
(3 - sqrt(2)) (3 + sqrt(2)) 7
(8 - sqrt(3)) (9 + sqrt(3)) 69 - sqrt(3)
------------- * ------------- = ----------------
(9 - sqrt(3)) (9 + sqrt(3)) 78
(3sqrt(2) - 5) (-2sqrt(7) + 6)
-------------- * --------------- = ----------------
(2sqrt(7) + 6) (-2sqrt(7) + 6)
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