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Simplifying x2 + 3x + -138 = 0 Reorder the terms: -138 + 3x + x2 = 0 Solving -138 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '138' to each side of the equation. -138 + 3x + 138 + x2 = 0 + 138 Reorder the terms: -138 + 138 + 3x + x2 = 0 + 138 Combine like terms: -138 + 138 = 0 0 + 3x + x2 = 0 + 138 3x + x2 = 0 + 138 Combine like terms: 0 + 138 = 138 3x + x2 = 138 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 = 138 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 138 + 2.25 Combine like terms: 138 + 2.25 = 140.25 2.25 + 3x + x2 = 140.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (x + 1.5) equal to 11.842719282 and -11.842719282.Subproblem 1
x + 1.5 = 11.842719282 Simplifying x + 1.5 = 11.842719282 Reorder the terms: 1.5 + x = 11.842719282 Solving 1.5 + x = 11.842719282 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 = 11.842719282 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 11.842719282 + -1.5 x = 11.842719282 + -1.5 Combine like terms: 11.842719282 + -1.5 = 10.342719282 x = 10.342719282 Simplifying x = 10.342719282Subproblem 2
x + 1.5 = -11.842719282 Simplifying x + 1.5 = -11.842719282 Reorder the terms: 1.5 + x = -11.842719282 Solving 1.5 + x = -11.842719282 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 = -11.842719282 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -11.842719282 + -1.5 x = -11.842719282 + -1.5 Combine like terms: -11.842719282 + -1.5 = -13.342719282 x = -13.342719282 Simplifying x = -13.342719282Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.342719282, -13.342719282}
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