Answer:
Explanation:
First Question
The top question has 2 solutions because eventually you will have to take the square root of (x - 4)^2. One square root will be plus, and the other minus
(x - 4)^2 - 28 = 8 Add 28 to both sides
(x - 4)^2 -28+28 = 8+28 Collect like terms
(x - 4)^2 = 36 Take the square root.
sqrt( (x - 4)^2 ) = sqrt(36)
x - 4 = +/- 6
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x - 4 = + 6
x = 6 + 4
x = 10
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x - 4 = - 6
x = - 6 + 4
x = - 2
The two solutions are (10,0) and (-2,0)
Second Question
The question is solved correctly up to the point where the square root needs to be taken. It is incorrect at that point.
x^2 - 6x - 7 = 0 Add 7 to both sides.
x^2 - 6x = 7 Add 1/2 the linear term and square it to both sides.
x^2 - 6x + (6/2)^2 = 7 + (6/2)^2 Expand the right
x^2 - 6x + 3^2 = 7 + 9
x^2 - 6x + 9 = 16 express the square on the left
(x - 3)^2 = 16 Take the sqrt of both sides.
x - 3 = sqrt(16)
x - 3 = +/-4
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x - 3 = 4
x = 4 + 3
x = 7
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x -3 = - 4
x = - 4 + 3
x = - 1
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Solutions
(7,0) and (-1,0)