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Simplifying x2 + -3x + -135 = 0 Reorder the terms: -135 + -3x + x2 = 0 Solving -135 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '135' to each side of the equation. -135 + -3x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + -3x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + -3x + x2 = 0 + 135 -3x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 -3x + x2 = 135 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 = 135 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 135 + 2.25 Combine like terms: 135 + 2.25 = 137.25 2.25 + -3x + x2 = 137.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 137.25 Calculate the square root of the right side: 11.715374514 Break this problem into two subproblems by setting (x + -1.5) equal to 11.715374514 and -11.715374514.Subproblem 1
x + -1.5 = 11.715374514 Simplifying x + -1.5 = 11.715374514 Reorder the terms: -1.5 + x = 11.715374514 Solving -1.5 + x = 11.715374514 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 = 11.715374514 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 11.715374514 + 1.5 x = 11.715374514 + 1.5 Combine like terms: 11.715374514 + 1.5 = 13.215374514 x = 13.215374514 Simplifying x = 13.215374514Subproblem 2
x + -1.5 = -11.715374514 Simplifying x + -1.5 = -11.715374514 Reorder the terms: -1.5 + x = -11.715374514 Solving -1.5 + x = -11.715374514 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 = -11.715374514 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -11.715374514 + 1.5 x = -11.715374514 + 1.5 Combine like terms: -11.715374514 + 1.5 = -10.215374514 x = -10.215374514 Simplifying x = -10.215374514Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.215374514, -10.215374514}
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