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This quadratic equation which will have two solutions can be solved by completing the square or by using the quadratic equation formula.Completing the square:x2+18x+4 = 0(x+9)2+4 = 0(x+9)2+4-81 = 0(x+9)2 = 77x+9 = + or - the square root of 77x = -9 + or - the square root of 77If you're not too sure about the procedure of completing the square your maths tutor should be familiar with it.
x2-18x+81 = (x-9)(x-9) when factored
81. To complete the square of x^2 + 18x, you take half the coefficient of the x term (half of 18 is 9), and square that number (9 squared is 81). To confirm this works, you can now factor x^2 + 18x + 81 and see that it factors as (x+9)(x+9), or (x+9)^2, a perfect square.
18x2 +12x + 2 this is not a perfect square trinomial so let's work a little bit here. 18x2 +12x + 2 factor 2 = 2(9x2 +6x + 1) = 2(3x + 1)2 represent 2 as (√2)2 = (√2)2(3x + 1)2 = [(√2)(3x + 1)]2 take its square root = (√2)(3x + 1) for all x > -1/3.
Factors are: 9(x - 1)(x - 1) or (3x - 3)2, so yes, it is.