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Simplifying 126.75 = (x + -6)(x + -6)(3) Reorder the terms: 126.75 = (-6 + x)(x + -6)(3) Reorder the terms: 126.75 = (-6 + x)(-6 + x)(3) Reorder the terms for easier multiplication: 126.75 = 3(-6 + x)(-6 + x) Multiply (-6 + x) * (-6 + x) 126.75 = 3(-6(-6 + x) + x(-6 + x)) 126.75 = 3((-6 * -6 + x * -6) + x(-6 + x)) 126.75 = 3((36 + -6x) + x(-6 + x)) 126.75 = 3(36 + -6x + (-6 * x + x * x)) 126.75 = 3(36 + -6x + (-6x + x2)) Combine like terms: -6x + -6x = -12x 126.75 = 3(36 + -12x + x2) 126.75 = (36 * 3 + -12x * 3 + x2 * 3) 126.75 = (108 + -36x + 3x2) Solving 126.75 = 108 + -36x + 3x2 Solving for variable 'x'. Combine like terms: 126.75 + -108 = 18.75 18.75 + 36x + -3x2 = 108 + -36x + 3x2 + -108 + 36x + -3x2 Reorder the terms: 18.75 + 36x + -3x2 = 108 + -108 + -36x + 36x + 3x2 + -3x2 Combine like terms: 108 + -108 = 0 18.75 + 36x + -3x2 = 0 + -36x + 36x + 3x2 + -3x2 18.75 + 36x + -3x2 = -36x + 36x + 3x2 + -3x2 Combine like terms: -36x + 36x = 0 18.75 + 36x + -3x2 = 0 + 3x2 + -3x2 18.75 + 36x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 18.75 + 36x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -6.25 + -12x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -12x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -12x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -12x + x2 = 0 + 6.25 -12x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -12x + x2 = 6.25 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 6.25 + 36 Reorder the terms: 36 + -12x + x2 = 6.25 + 36 Combine like terms: 6.25 + 36 = 42.25 36 + -12x + x2 = 42.25 Factor a perfect square on the left side: (x + -6)(x + -6) = 42.25 Calculate the square root of the right side: 6.5 Break this problem into two subproblems by setting (x + -6) equal to 6.5 and -6.5.Subproblem 1
x + -6 = 6.5 Simplifying x + -6 = 6.5 Reorder the terms: -6 + x = 6.5 Solving -6 + x = 6.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 6.5 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.5 + 6 x = 6.5 + 6 Combine like terms: 6.5 + 6 = 12.5 x = 12.5 Simplifying x = 12.5Subproblem 2
x + -6 = -6.5 Simplifying x + -6 = -6.5 Reorder the terms: -6 + x = -6.5 Solving -6 + x = -6.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -6.5 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.5 + 6 x = -6.5 + 6 Combine like terms: -6.5 + 6 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.5, -0.5}
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