9th grade algebra (completing square)
posted by Alexis
Can you check the following?
A1. (2x + 3)^2 = 25
sqrt(2x + 3)^2 = +sqrt(25)
2x + 3 = + 5
2x + 3 = 5, 2x + 3 = 5
2x = 2, 2x = 8
x = 1, x = 4
{4, 1}
A2. x^2 + 14x + 45 = 0
x^2 + 14x + __ = 45 + __
x^2 + 14x + 49 = 45 + 49
(x +7)^2 = 4
sqrt(x+7)^2 = + sqrt(4)
x + 7 = + 2
x + 7 = 2, x +7 = 2
x = 5, x = 9
{9, 5}
B2. 3x^2 + 12x  1 = 14
3x^2 + 12x + __ = 14 + 1
3(x^2 + 4x + __) = 15 + __
3(x^2 + 4x + 4) = 15 + 12
3(x + 2)^2 = 27
(x + 2)^2 = 9
sqrt(x+2)^2 = + sqrt(9)
x + 2 = + 3
x + 2 = 3, x + 2 = 3
x = 1, x = 5
{5, 1}
C1. 3x^2  12x  66 = 3
3x^2  12x + __ = 3 + 66
3x^2  12x + __ = 63
3(x^2  4x + 4) = 63 + 12
3(x  2)^2 = 75
(x  2)^2 = 25
sqrt(x2)^2 = + sqrt(25)
x  2 = + 5
x  2 = 5, x  2 = 5
x = 7, x = 3
{3, 7}
D1. 2x^2  12x  11 = 3
2x^2  12x + __ = 3 + 11
2x^2  12x + __ = 14 + __
2(x^2  6x + 9) = 14 + 18
2(x3)^2 = 32
(x3)^2 = 16
sqrt(x3)2 = + sqrt(16)
x  3 = + 4
x  3 = 4, x  3 = 4
x = 7, x = 1
{1, 7}
D2. (x+4)^2 = 49
sqrt(x+4)^2 = + sqrt(49)
x + 4 = + 7
x + 4 = 7, x + 4 = 7
x = 3, x = 11
{11, 3}
E1. 4x^2 + 16x + 11 = 4
4x^2 + 16x + __ = 4  11
4x^2 + 16x + __ = 7 + __
4(x^2 + 4x + 4) = 7 + 16
4(x+2)^2 = 9
(x+2)^2 = 9/4
sqrt(x+2)^2 = + sqrt(9/4)
x + 2 = + 3/2
x + 2 = 3/2, x + 2 = 3/2
x = 1/2, x = 7/2
{7/2, 1/2}
E2. x^2  16x = 63
(x^2  16x + 64) = 63 + 64
(x  8)^2 = 1
sqrt(x  8)^2 = + sqrt(1)
x  8 = + 1
x  8 = 1, x  8 = 1
x = 9, x = 7
{7,9}
F2. x^2 + 8x  63 = 21
x^2 + 8x + __ = 21 + 63
x^2 + 8x + 16 = 84 + 16
(x + 4)^2 = 100
sqrt(x + 4)^2 = + sqrt(100)
x + 4 = 10, x + 4 = 10
x = 6, x = 14
{14, 6}
G1. (4x  1)^2 = 81
sqrt(4x1)^2 = + sqrt(81)
4x  1 = + 9
4x  1 = 9, 4x 1 = 9
4x = 10 , 4x = 8
x = 10/4 , 4x = 2
x = 5/2
{2, 5/2}
G2. x^2 + 10x + 13 = 3
x^2 + 10x + __ = 3  13
x^2 + 10x + 25 = 16 + 25
sqrt(x + 5)^2 = + sqrt(9)
x + 5 = 3, x + 5 = 3
x = 2, x = 8
{8, 2}
H1. x^2  2x + 3 = 27
x^2  2x + __ = 27  3
x^2  2x + 1 = 24 + 1
(x  1)^2 = 25
sqrt(x  1)^2 = + sqrt(25)
x  1 = + 5
x  1 = 5, x  1 = 5
x = 6, x = 4
{4, 6}
H2. 9x^2  18x  18 = 2
9x^2  18x + __ =  2 + 18 + __
9(x^2  2x + 1) = 16 + 9
9(x1)^2 = 25
(x1)^2 = 25/9
sqrt(x1)^2 = + sqrt(25/9)
x  1 = + 5/3
x  1 = 5/3, x  1 = 5/3
x = 8/3, x = 2/3
{2/3, 8/3}

Reiny
You seem to have a good grasp of doing these.
I verified most of your answers by subbing them back into the original equation.
All the ones I tried were correct.
I suggest you take your calculator and test your answers. 
Alexis
Thanks for checking. For the ones above, they didn't match any anwers from the homework puzzle. So, I wasn't sure I was doing them correctly.
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