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Simplifying x2 + 3x + -118 = 0 Reorder the terms: -118 + 3x + x2 = 0 Solving -118 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '118' to each side of the equation. -118 + 3x + 118 + x2 = 0 + 118 Reorder the terms: -118 + 118 + 3x + x2 = 0 + 118 Combine like terms: -118 + 118 = 0 0 + 3x + x2 = 0 + 118 3x + x2 = 0 + 118 Combine like terms: 0 + 118 = 118 3x + x2 = 118 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 = 118 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 118 + 2.25 Combine like terms: 118 + 2.25 = 120.25 2.25 + 3x + x2 = 120.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + 1.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + 1.5 = 10.9658561 Simplifying x + 1.5 = 10.9658561 Reorder the terms: 1.5 + x = 10.9658561 Solving 1.5 + x = 10.9658561 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 = 10.9658561 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.9658561 + -1.5 x = 10.9658561 + -1.5 Combine like terms: 10.9658561 + -1.5 = 9.4658561 x = 9.4658561 Simplifying x = 9.4658561Subproblem 2
x + 1.5 = -10.9658561 Simplifying x + 1.5 = -10.9658561 Reorder the terms: 1.5 + x = -10.9658561 Solving 1.5 + x = -10.9658561 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 = -10.9658561 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.9658561 + -1.5 x = -10.9658561 + -1.5 Combine like terms: -10.9658561 + -1.5 = -12.4658561 x = -12.4658561 Simplifying x = -12.4658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.4658561, -12.4658561}
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