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Simplifying (x2 + 3x + -187) = 0 Reorder the terms: (-187 + 3x + x2) = 0 Remove parenthesis around (-187 + 3x + x2) -187 + 3x + x2 = 0 Solving -187 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '187' to each side of the equation. -187 + 3x + 187 + x2 = 0 + 187 Reorder the terms: -187 + 187 + 3x + x2 = 0 + 187 Combine like terms: -187 + 187 = 0 0 + 3x + x2 = 0 + 187 3x + x2 = 0 + 187 Combine like terms: 0 + 187 = 187 3x + x2 = 187 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 = 187 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 187 + 2.25 Combine like terms: 187 + 2.25 = 189.25 2.25 + 3x + x2 = 189.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 189.25 Calculate the square root of the right side: 13.756816492 Break this problem into two subproblems by setting (x + 1.5) equal to 13.756816492 and -13.756816492.Subproblem 1
x + 1.5 = 13.756816492 Simplifying x + 1.5 = 13.756816492 Reorder the terms: 1.5 + x = 13.756816492 Solving 1.5 + x = 13.756816492 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 = 13.756816492 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 13.756816492 + -1.5 x = 13.756816492 + -1.5 Combine like terms: 13.756816492 + -1.5 = 12.256816492 x = 12.256816492 Simplifying x = 12.256816492Subproblem 2
x + 1.5 = -13.756816492 Simplifying x + 1.5 = -13.756816492 Reorder the terms: 1.5 + x = -13.756816492 Solving 1.5 + x = -13.756816492 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 = -13.756816492 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -13.756816492 + -1.5 x = -13.756816492 + -1.5 Combine like terms: -13.756816492 + -1.5 = -15.256816492 x = -15.256816492 Simplifying x = -15.256816492Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.256816492, -15.256816492}
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