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Simplifying (x + -6)(3x) + 5 = (x + 4)(x) Reorder the terms: (-6 + x)(3x) + 5 = (x + 4)(x) Remove parenthesis around (3x) (-6 + x) * 3x + 5 = (x + 4)(x) Reorder the terms for easier multiplication: 3x(-6 + x) + 5 = (x + 4)(x) (-6 * 3x + x * 3x) + 5 = (x + 4)(x) (-18x + 3x2) + 5 = (x + 4)(x) Reorder the terms: 5 + -18x + 3x2 = (x + 4)(x) Reorder the terms: 5 + -18x + 3x2 = (4 + x)(x) Reorder the terms for easier multiplication: 5 + -18x + 3x2 = x(4 + x) 5 + -18x + 3x2 = (4 * x + x * x) 5 + -18x + 3x2 = (4x + x2) Solving 5 + -18x + 3x2 = 4x + x2 Solving for variable 'x'. Reorder the terms: 5 + -18x + -4x + 3x2 + -1x2 = 4x + x2 + -4x + -1x2 Combine like terms: -18x + -4x = -22x 5 + -22x + 3x2 + -1x2 = 4x + x2 + -4x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 5 + -22x + 2x2 = 4x + x2 + -4x + -1x2 Reorder the terms: 5 + -22x + 2x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 5 + -22x + 2x2 = 0 + x2 + -1x2 5 + -22x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + -22x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -11x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -11x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -11x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -11x + x2 = 0 + -2.5 -11x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -11x + x2 = -2.5 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -2.5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -2.5 + 30.25 Combine like terms: -2.5 + 30.25 = 27.75 30.25 + -11x + x2 = 27.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 27.75 Calculate the square root of the right side: 5.267826876 Break this problem into two subproblems by setting (x + -5.5) equal to 5.267826876 and -5.267826876.Subproblem 1
x + -5.5 = 5.267826876 Simplifying x + -5.5 = 5.267826876 Reorder the terms: -5.5 + x = 5.267826876 Solving -5.5 + x = 5.267826876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.267826876 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.267826876 + 5.5 x = 5.267826876 + 5.5 Combine like terms: 5.267826876 + 5.5 = 10.767826876 x = 10.767826876 Simplifying x = 10.767826876Subproblem 2
x + -5.5 = -5.267826876 Simplifying x + -5.5 = -5.267826876 Reorder the terms: -5.5 + x = -5.267826876 Solving -5.5 + x = -5.267826876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.267826876 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.267826876 + 5.5 x = -5.267826876 + 5.5 Combine like terms: -5.267826876 + 5.5 = 0.232173124 x = 0.232173124 Simplifying x = 0.232173124Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.767826876, 0.232173124}
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