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Simplifying x2 + -3x + -36 = 1 Reorder the terms: -36 + -3x + x2 = 1 Solving -36 + -3x + x2 = 1 Solving for variable 'x'. Reorder the terms: -36 + -1 + -3x + x2 = 1 + -1 Combine like terms: -36 + -1 = -37 -37 + -3x + x2 = 1 + -1 Combine like terms: 1 + -1 = 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 = 7.764982043 x = 7.764982043 Simplifying x = 7.764982043Subproblem 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 = -4.764982043 x = -4.764982043 Simplifying x = -4.764982043Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.764982043, -4.764982043}
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