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Simplifying 2(x + 2)(x + -3) = 3(x + 1)(x + -6) + 4 Reorder the terms: 2(2 + x)(x + -3) = 3(x + 1)(x + -6) + 4 Reorder the terms: 2(2 + x)(-3 + x) = 3(x + 1)(x + -6) + 4 Multiply (2 + x) * (-3 + x) 2(2(-3 + x) + x(-3 + x)) = 3(x + 1)(x + -6) + 4 2((-3 * 2 + x * 2) + x(-3 + x)) = 3(x + 1)(x + -6) + 4 2((-6 + 2x) + x(-3 + x)) = 3(x + 1)(x + -6) + 4 2(-6 + 2x + (-3 * x + x * x)) = 3(x + 1)(x + -6) + 4 2(-6 + 2x + (-3x + x2)) = 3(x + 1)(x + -6) + 4 Combine like terms: 2x + -3x = -1x 2(-6 + -1x + x2) = 3(x + 1)(x + -6) + 4 (-6 * 2 + -1x * 2 + x2 * 2) = 3(x + 1)(x + -6) + 4 (-12 + -2x + 2x2) = 3(x + 1)(x + -6) + 4 Reorder the terms: -12 + -2x + 2x2 = 3(1 + x)(x + -6) + 4 Reorder the terms: -12 + -2x + 2x2 = 3(1 + x)(-6 + x) + 4 Multiply (1 + x) * (-6 + x) -12 + -2x + 2x2 = 3(1(-6 + x) + x(-6 + x)) + 4 -12 + -2x + 2x2 = 3((-6 * 1 + x * 1) + x(-6 + x)) + 4 -12 + -2x + 2x2 = 3((-6 + 1x) + x(-6 + x)) + 4 -12 + -2x + 2x2 = 3(-6 + 1x + (-6 * x + x * x)) + 4 -12 + -2x + 2x2 = 3(-6 + 1x + (-6x + x2)) + 4 Combine like terms: 1x + -6x = -5x -12 + -2x + 2x2 = 3(-6 + -5x + x2) + 4 -12 + -2x + 2x2 = (-6 * 3 + -5x * 3 + x2 * 3) + 4 -12 + -2x + 2x2 = (-18 + -15x + 3x2) + 4 Reorder the terms: -12 + -2x + 2x2 = -18 + 4 + -15x + 3x2 Combine like terms: -18 + 4 = -14 -12 + -2x + 2x2 = -14 + -15x + 3x2 Solving -12 + -2x + 2x2 = -14 + -15x + 3x2 Solving for variable 'x'. Reorder the terms: -12 + 14 + -2x + 15x + 2x2 + -3x2 = -14 + -15x + 3x2 + 14 + 15x + -3x2 Combine like terms: -12 + 14 = 2 2 + -2x + 15x + 2x2 + -3x2 = -14 + -15x + 3x2 + 14 + 15x + -3x2 Combine like terms: -2x + 15x = 13x 2 + 13x + 2x2 + -3x2 = -14 + -15x + 3x2 + 14 + 15x + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 2 + 13x + -1x2 = -14 + -15x + 3x2 + 14 + 15x + -3x2 Reorder the terms: 2 + 13x + -1x2 = -14 + 14 + -15x + 15x + 3x2 + -3x2 Combine like terms: -14 + 14 = 0 2 + 13x + -1x2 = 0 + -15x + 15x + 3x2 + -3x2 2 + 13x + -1x2 = -15x + 15x + 3x2 + -3x2 Combine like terms: -15x + 15x = 0 2 + 13x + -1x2 = 0 + 3x2 + -3x2 2 + 13x + -1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 2 + 13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -13x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -13x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -13x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -13x + x2 = 0 + 2 -13x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -13x + x2 = 2 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 2 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 2 + 42.25 Combine like terms: 2 + 42.25 = 44.25 42.25 + -13x + x2 = 44.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + -6.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + -6.5 = 6.652067348 Simplifying x + -6.5 = 6.652067348 Reorder the terms: -6.5 + x = 6.652067348 Solving -6.5 + x = 6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 6.652067348 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.652067348 + 6.5 x = 6.652067348 + 6.5 Combine like terms: 6.652067348 + 6.5 = 13.152067348 x = 13.152067348 Simplifying x = 13.152067348Subproblem 2
x + -6.5 = -6.652067348 Simplifying x + -6.5 = -6.652067348 Reorder the terms: -6.5 + x = -6.652067348 Solving -6.5 + x = -6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -6.652067348 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.652067348 + 6.5 x = -6.652067348 + 6.5 Combine like terms: -6.652067348 + 6.5 = -0.152067348 x = -0.152067348 Simplifying x = -0.152067348Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.152067348, -0.152067348}
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