completing the square and more?

Question

1a)express x^2 - 6x + 7 in the form (x+a)^2 + b, finding the values of a and b

1b) find the range of values of x for which x^2 - 6x + 7 is less than 0

2a) express x^2 + 4x -5 in the form (x+a)^2 + b, finding the values of the constants a and b

2b) find the values of x for which x^2 + 4x - 5 is greater than 0

Answer 1

Completing the square

x² - 6x + 7 = 0

Transpose 7

x² - 6x + 7 - 7 = 0 - 7

x² - 6x = - 7

x² - 6x +_____= - 7 + _____

x² - 6x + 9 = - 7 + 9

x² - 6x + 9 = 2

(x - 3)(x - 3) = 2

(x - 3)² = 2

(√x - 3)² = ± √2

x - 3 = ± √ 2

Transpose 3

x - 3 + 3 = 3 ± √2

x = 3 ± √2

x = 3 ± 1.414213562

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Solving for +

x = 3 + 1.414213562

x = 4.414213562

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Solving for -

x = 3 - 1.414213562

x = 1.585786438

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