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}

9th grade algebra (completing square) 
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. 
9th grade algebra (completing square) 
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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