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Simplifying x(x + 3) = 265 Reorder the terms: x(3 + x) = 265 (3 * x + x * x) = 265 (3x + x2) = 265 Solving 3x + x2 = 265 Solving for variable 'x'. Reorder the terms: -265 + 3x + x2 = 265 + -265 Combine like terms: 265 + -265 = 0 -265 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '265' to each side of the equation. -265 + 3x + 265 + x2 = 0 + 265 Reorder the terms: -265 + 265 + 3x + x2 = 0 + 265 Combine like terms: -265 + 265 = 0 0 + 3x + x2 = 0 + 265 3x + x2 = 0 + 265 Combine like terms: 0 + 265 = 265 3x + x2 = 265 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 = 265 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 265 + 2.25 Combine like terms: 265 + 2.25 = 267.25 2.25 + 3x + x2 = 267.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 267.25 Calculate the square root of the right side: 16.347782724 Break this problem into two subproblems by setting (x + 1.5) equal to 16.347782724 and -16.347782724.Subproblem 1
x + 1.5 = 16.347782724 Simplifying x + 1.5 = 16.347782724 Reorder the terms: 1.5 + x = 16.347782724 Solving 1.5 + x = 16.347782724 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 = 16.347782724 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 16.347782724 + -1.5 x = 16.347782724 + -1.5 Combine like terms: 16.347782724 + -1.5 = 14.847782724 x = 14.847782724 Simplifying x = 14.847782724Subproblem 2
x + 1.5 = -16.347782724 Simplifying x + 1.5 = -16.347782724 Reorder the terms: 1.5 + x = -16.347782724 Solving 1.5 + x = -16.347782724 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 = -16.347782724 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -16.347782724 + -1.5 x = -16.347782724 + -1.5 Combine like terms: -16.347782724 + -1.5 = -17.847782724 x = -17.847782724 Simplifying x = -17.847782724Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.847782724, -17.847782724}
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