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Simplifying (3x + 3)(x) = 592 Reorder the terms: (3 + 3x)(x) = 592 Reorder the terms for easier multiplication: x(3 + 3x) = 592 (3 * x + 3x * x) = 592 (3x + 3x2) = 592 Solving 3x + 3x2 = 592 Solving for variable 'x'. Reorder the terms: -592 + 3x + 3x2 = 592 + -592 Combine like terms: 592 + -592 = 0 -592 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -197.3333333 + x + x2 = 0 Move the constant term to the right: Add '197.3333333' to each side of the equation. -197.3333333 + x + 197.3333333 + x2 = 0 + 197.3333333 Reorder the terms: -197.3333333 + 197.3333333 + x + x2 = 0 + 197.3333333 Combine like terms: -197.3333333 + 197.3333333 = 0.0000000 0.0000000 + x + x2 = 0 + 197.3333333 x + x2 = 0 + 197.3333333 Combine like terms: 0 + 197.3333333 = 197.3333333 x + x2 = 197.3333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 197.3333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 197.3333333 + 0.25 Combine like terms: 197.3333333 + 0.25 = 197.5833333 1.25 + x2 = 197.5833333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 197.5833333 Calculate the square root of the right side: 14.056433876 Break this problem into two subproblems by setting (x + 0.5) equal to 14.056433876 and -14.056433876.Subproblem 1
x + 0.5 = 14.056433876 Simplifying x + 0.5 = 14.056433876 Reorder the terms: 0.5 + x = 14.056433876 Solving 0.5 + x = 14.056433876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 14.056433876 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.056433876 + -0.5 x = 14.056433876 + -0.5 Combine like terms: 14.056433876 + -0.5 = 13.556433876 x = 13.556433876 Simplifying x = 13.556433876Subproblem 2
x + 0.5 = -14.056433876 Simplifying x + 0.5 = -14.056433876 Reorder the terms: 0.5 + x = -14.056433876 Solving 0.5 + x = -14.056433876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -14.056433876 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.056433876 + -0.5 x = -14.056433876 + -0.5 Combine like terms: -14.056433876 + -0.5 = -14.556433876 x = -14.556433876 Simplifying x = -14.556433876Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.556433876, -14.556433876}
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