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Simplifying x(x + 3) = 37 Reorder the terms: x(3 + x) = 37 (3 * x + x * x) = 37 (3x + x2) = 37 Solving 3x + x2 = 37 Solving for variable 'x'. Reorder the terms: -37 + 3x + x2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 3x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + 3x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 3x + x2 = 0 + 37 3x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 3x + x2 = 37 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 = 37 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 37 + 2.25 Combine like terms: 37 + 2.25 = 39.25 2.25 + 3x + x2 = 39.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x + 1.5) equal to 6.264982043 and -6.264982043.Subproblem 1
x + 1.5 = 6.264982043 Simplifying x + 1.5 = 6.264982043 Reorder the terms: 1.5 + x = 6.264982043 Solving 1.5 + x = 6.264982043 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 = 6.264982043 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.264982043 + -1.5 x = 6.264982043 + -1.5 Combine like terms: 6.264982043 + -1.5 = 4.764982043 x = 4.764982043 Simplifying x = 4.764982043Subproblem 2
x + 1.5 = -6.264982043 Simplifying x + 1.5 = -6.264982043 Reorder the terms: 1.5 + x = -6.264982043 Solving 1.5 + x = -6.264982043 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 = -6.264982043 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.264982043 + -1.5 x = -6.264982043 + -1.5 Combine like terms: -6.264982043 + -1.5 = -7.764982043 x = -7.764982043 Simplifying x = -7.764982043Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.764982043, -7.764982043}
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