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Question 173002: [] means a blank spot..
'means # is exponent...
Complete the square.
1. x'2 + 60x + []
2. x'2 – 7x + []
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Solve each equation by completing the square.
3. x'2 – 6x – 16 = 0
4. x'2 – 14x + 74 = 0
5. 3x'2 + 5x – 28 = 0
6. 4x'2 – 6x + 3 = 0
please write the answers. im really needy
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Complete the square.
1. x'2 + 60x + []
Take 1/2 the 'b' coefficient (60) and square it:
(1/2)(60) = 30
square that:
30^2 = 900
x'2 + 60x + 900
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2. x'2 – 7x + []
(1/2)(-7) = -7/2
square that:
49/4
x'2 – 7x + 49/4
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Solve each equation by completing the square.
3. x'2 – 6x – 16 = 0
x'2 – 6x = 16
x'2 – 6x + 9 = 16 + 9
(x-3)^2 = 25
x-3 = (+-)5
x = (+-)5+3
x = {-2, 8}
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4. x'2 – 14x + 74 = 0
x'2 – 14x = -74
x'2 – 14x + 49 = -74 +49
(x-7)^2 = -25
x-7 = (+-)5i
x = (+-)5i + 7
x = {(7+5i), (7-5i)}
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5. 3x'2 + 5x – 28 = 0
3x'2 + 5x = 28
3(x'2 + (5/3)x) = 28
3(x'2 + (5/3)x + 25/36) = 28 + 25/13
3(x+ 5/6)^2 = 364/13 + 25/13
3(x+ 5/6)^2 = 389/13
(x+ 5/6)^2 = 389/39
x+ 5/6 = (+-)3.1582
x = {-3.992, 2.325}
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6. 4x'2 – 6x + 3 = 0
4x'2 – 6x = -3
4(x'2 – (6/4)x) = -3
4(x'2 – (6/4)x + 9/16) = -3 + 9/4
4(x + 3/4)^2 = -12/4 + 9/4
4(x + 3/4)^2 = -2/4
(x + 3/4)^2 = -2/8
(x + 3/4)^2 = -1/4
x + 3/4 = (+-)1/2i
x = (+-).5i - 3/4
x = {(-3/4 + .5i), (-3/4 - .5i)}
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