Question 59982This question is from textbook college algebra
: x^2-4x+4=49
(3x-6)^2=4x^2
(x-1)^2+(x^2+1)-12=0
This question is from textbook college algebra
Answer by uma(370)   (Show Source):
You can put this solution on YOUR website! 1. x^2 - 4x + 4 = 49
==> x^2 - 4x + 4 - 49 = 0 [Adding -49 to both the sides]
==> x^2 - 4x - 45 = 0
==> x^2 - 9x + 5x - 45 = 0 [Splitting the middle term so that the product is 45]
==> x(x-9) + 5(x - 9) = 0
==> (x - 9)(x+5) = 0
==> x-9 = 0 or x + 5 = 0
==> x = 9 or x = -5
2. (3x-6)^2 = 4x^2
==> (3x)^2 -2(3x)(6) + 6^2 = 4x^2 [expanding(3x-6)^2 using the formula]
==> 9x^2-36x + 36 = 4x^2
==> 9x^2 - 4x^2 - 36x + 36 = 0 [Adding -4x^2 to both the sides]
==> 5x^2 - 36x + 36 = 0
==> 5x^2 - 30x - 6x + 36 = 0 [Splitting the middle term so that the product is 5*36 = 180]
==> 5x(x-6) - 6(x-6) = 0
==> (x-6)(5x-6) = 0
==> (x-6) = 0 or (5x - 6) = 0
==> x = 6 or 5x = 6
==> x = 6 or x =6/5
3. (x-1)^2 + x^2+1 - 12 = 0
==> x^2 -2x + 1 + x^2 + 1 - 12 = 0 [expanding(x-1)^2 using the formula]
==> 2x^2 - 2x - 10 = 0
==> x^2 - x - 5 = 0 [dividing by 2 throughout]
As the above expression cannot be factorised, use the formula to solve for x
==> x = [-b+/- sqrt(b^2-4ac)]/2a
==> x = [1+/-sqrt(1 + 20)]/2
==> x = 1+/-sqrt(21)]/2
Good Luck!!!
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