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Simplifying (x + 3)(x + 6) = (2x + 2)(x + -6) Reorder the terms: (3 + x)(x + 6) = (2x + 2)(x + -6) Reorder the terms: (3 + x)(6 + x) = (2x + 2)(x + -6) Multiply (3 + x) * (6 + x) (3(6 + x) + x(6 + x)) = (2x + 2)(x + -6) ((6 * 3 + x * 3) + x(6 + x)) = (2x + 2)(x + -6) ((18 + 3x) + x(6 + x)) = (2x + 2)(x + -6) (18 + 3x + (6 * x + x * x)) = (2x + 2)(x + -6) (18 + 3x + (6x + x2)) = (2x + 2)(x + -6) Combine like terms: 3x + 6x = 9x (18 + 9x + x2) = (2x + 2)(x + -6) Reorder the terms: 18 + 9x + x2 = (2 + 2x)(x + -6) Reorder the terms: 18 + 9x + x2 = (2 + 2x)(-6 + x) Multiply (2 + 2x) * (-6 + x) 18 + 9x + x2 = (2(-6 + x) + 2x * (-6 + x)) 18 + 9x + x2 = ((-6 * 2 + x * 2) + 2x * (-6 + x)) 18 + 9x + x2 = ((-12 + 2x) + 2x * (-6 + x)) 18 + 9x + x2 = (-12 + 2x + (-6 * 2x + x * 2x)) 18 + 9x + x2 = (-12 + 2x + (-12x + 2x2)) Combine like terms: 2x + -12x = -10x 18 + 9x + x2 = (-12 + -10x + 2x2) Solving 18 + 9x + x2 = -12 + -10x + 2x2 Solving for variable 'x'. Reorder the terms: 18 + 12 + 9x + 10x + x2 + -2x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2 Combine like terms: 18 + 12 = 30 30 + 9x + 10x + x2 + -2x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2 Combine like terms: 9x + 10x = 19x 30 + 19x + x2 + -2x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2 Combine like terms: x2 + -2x2 = -1x2 30 + 19x + -1x2 = -12 + -10x + 2x2 + 12 + 10x + -2x2 Reorder the terms: 30 + 19x + -1x2 = -12 + 12 + -10x + 10x + 2x2 + -2x2 Combine like terms: -12 + 12 = 0 30 + 19x + -1x2 = 0 + -10x + 10x + 2x2 + -2x2 30 + 19x + -1x2 = -10x + 10x + 2x2 + -2x2 Combine like terms: -10x + 10x = 0 30 + 19x + -1x2 = 0 + 2x2 + -2x2 30 + 19x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 30 + 19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + -19x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -19x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -19x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -19x + x2 = 0 + 30 -19x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -19x + x2 = 30 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 30 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 30 + 90.25 Combine like terms: 30 + 90.25 = 120.25 90.25 + -19x + x2 = 120.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + -9.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + -9.5 = 10.9658561 Simplifying x + -9.5 = 10.9658561 Reorder the terms: -9.5 + x = 10.9658561 Solving -9.5 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 10.9658561 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 10.9658561 + 9.5 x = 10.9658561 + 9.5 Combine like terms: 10.9658561 + 9.5 = 20.4658561 x = 20.4658561 Simplifying x = 20.4658561Subproblem 2
x + -9.5 = -10.9658561 Simplifying x + -9.5 = -10.9658561 Reorder the terms: -9.5 + x = -10.9658561 Solving -9.5 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -10.9658561 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -10.9658561 + 9.5 x = -10.9658561 + 9.5 Combine like terms: -10.9658561 + 9.5 = -1.4658561 x = -1.4658561 Simplifying x = -1.4658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.4658561, -1.4658561}
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