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Simplifying x(x + 3) = 1080 Reorder the terms: x(3 + x) = 1080 (3 * x + x * x) = 1080 (3x + x2) = 1080 Solving 3x + x2 = 1080 Solving for variable 'x'. Reorder the terms: -1080 + 3x + x2 = 1080 + -1080 Combine like terms: 1080 + -1080 = 0 -1080 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1080' to each side of the equation. -1080 + 3x + 1080 + x2 = 0 + 1080 Reorder the terms: -1080 + 1080 + 3x + x2 = 0 + 1080 Combine like terms: -1080 + 1080 = 0 0 + 3x + x2 = 0 + 1080 3x + x2 = 0 + 1080 Combine like terms: 0 + 1080 = 1080 3x + x2 = 1080 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 = 1080 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1080 + 2.25 Combine like terms: 1080 + 2.25 = 1082.25 2.25 + 3x + x2 = 1082.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1082.25 Calculate the square root of the right side: 32.897568299 Break this problem into two subproblems by setting (x + 1.5) equal to 32.897568299 and -32.897568299.Subproblem 1
x + 1.5 = 32.897568299 Simplifying x + 1.5 = 32.897568299 Reorder the terms: 1.5 + x = 32.897568299 Solving 1.5 + x = 32.897568299 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 = 32.897568299 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 32.897568299 + -1.5 x = 32.897568299 + -1.5 Combine like terms: 32.897568299 + -1.5 = 31.397568299 x = 31.397568299 Simplifying x = 31.397568299Subproblem 2
x + 1.5 = -32.897568299 Simplifying x + 1.5 = -32.897568299 Reorder the terms: 1.5 + x = -32.897568299 Solving 1.5 + x = -32.897568299 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 = -32.897568299 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -32.897568299 + -1.5 x = -32.897568299 + -1.5 Combine like terms: -32.897568299 + -1.5 = -34.397568299 x = -34.397568299 Simplifying x = -34.397568299Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.397568299, -34.397568299}
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