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Simplifying x2 + 3x = 31 Reorder the terms: 3x + x2 = 31 Solving 3x + x2 = 31 Solving for variable 'x'. Reorder the terms: -31 + 3x + x2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 3x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 3x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 3x + x2 = 0 + 31 3x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 3x + x2 = 31 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 = 31 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 31 + 2.25 Combine like terms: 31 + 2.25 = 33.25 2.25 + 3x + x2 = 33.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + 1.5) equal to 5.766281297 and -5.766281297.Subproblem 1
x + 1.5 = 5.766281297 Simplifying x + 1.5 = 5.766281297 Reorder the terms: 1.5 + x = 5.766281297 Solving 1.5 + x = 5.766281297 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 = 5.766281297 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.766281297 + -1.5 x = 5.766281297 + -1.5 Combine like terms: 5.766281297 + -1.5 = 4.266281297 x = 4.266281297 Simplifying x = 4.266281297Subproblem 2
x + 1.5 = -5.766281297 Simplifying x + 1.5 = -5.766281297 Reorder the terms: 1.5 + x = -5.766281297 Solving 1.5 + x = -5.766281297 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 = -5.766281297 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.766281297 + -1.5 x = -5.766281297 + -1.5 Combine like terms: -5.766281297 + -1.5 = -7.266281297 x = -7.266281297 Simplifying x = -7.266281297Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.266281297, -7.266281297}
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