SOLUTION: 1. Find solutions to x^2-x-12=0 The sum of the solutions is what 2. Find solutions to x^2+8x+15=0 The sum is what 3. Length of one leg of right triangle is 9m. The hypotenu

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Question 182105: 1. Find solutions to x^2-x-12=0 The sum of the solutions is what
2. Find solutions to x^2+8x+15=0 The sum is what
3. Length of one leg of right triangle is 9m. The hypotenuse is 3m more than the other leg. Find the length of the hypotenuse

4. Ten more than the square of a number is seven times the number. Find all
Answer by eperette(173) (Show Source):
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(1)
x^2 - x - 12= 0
(x - 4)(x + 3)= 0
x-4=0
x-4+4=0+4
x+0 = 4
x=4
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x+3=0
x+3-3=0-3
x+0=-3
x=-3
answer: x=4 or x=-3
(2)
x^2 + 8x + 15 =0
(x + 3)(x + 5)=0
x+3=0
x+3-3=0-3
x=-3
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x+5=0
x+5-5=0-5
x=-5
answer: x=-3 or x=-5
(3)
LET
leg DISABLED_event_one= x
leg two=y
hypotenuse=h
x=9
h=y+3
Know: x^2 + y^2 = h^2
9^2 + y^2 = (y+3)^2
81 + y^2 = (y+3)(y+3)
81 + y^2 = y(y+3) + 3(y+3)
81 + y^2 = y(y) + y(3) + 3(y) + 3(3)
81 + y^2 = y^2 + 3y + 3y +9
81 + y^2 = y^2 + 6y + 9
81 + y^2 -y^2 = y^2 - y^2 + 6y + 9
81 + 0 = 0 + 6y + 9
81 -9 = 6y + 9 - 9
72 = 6y + 0
72/6 = 6y/6
12 = y
Then h=y+3 = 12+ 3 = 15
(4)
Ten more than the square of a number is seven times the number. Find all
x^2 + 10 = 7x
x^2 + 10 - 7x = 7x - 7x
x^2 + 10 - 7x =0
x^2 - 7x + 10 = 0
(x - 5)(x -2) = 0
x-5=0
x-5+5 = 0+5
x = 5
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x-2=0
x-2+2=0+2
x=2
answer: x=5 or x=2