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Simplifying x(x + 3) = 120 Reorder the terms: x(3 + x) = 120 (3 * x + x * x) = 120 (3x + x2) = 120 Solving 3x + x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 3x + x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 3x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 3x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 3x + x2 = 0 + 120 3x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 3x + x2 = 120 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 120 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 120 + 2.25 Combine like terms: 120 + 2.25 = 122.25 2.25 + 3x + x2 = 122.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 122.25 Calculate the square root of the right side: 11.056672194 Break this problem into two subproblems by setting (x + 1.5) equal to 11.056672194 and -11.056672194.Subproblem 1
x + 1.5 = 11.056672194 Simplifying x + 1.5 = 11.056672194 Reorder the terms: 1.5 + x = 11.056672194 Solving 1.5 + x = 11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 11.056672194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 11.056672194 + -1.5 x = 11.056672194 + -1.5 Combine like terms: 11.056672194 + -1.5 = 9.556672194 x = 9.556672194 Simplifying x = 9.556672194Subproblem 2
x + 1.5 = -11.056672194 Simplifying x + 1.5 = -11.056672194 Reorder the terms: 1.5 + x = -11.056672194 Solving 1.5 + x = -11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -11.056672194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -11.056672194 + -1.5 x = -11.056672194 + -1.5 Combine like terms: -11.056672194 + -1.5 = -12.556672194 x = -12.556672194 Simplifying x = -12.556672194Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.556672194, -12.556672194}
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