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Simplifying x2 + 3x + -188 = 0 Reorder the terms: -188 + 3x + x2 = 0 Solving -188 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '188' to each side of the equation. -188 + 3x + 188 + x2 = 0 + 188 Reorder the terms: -188 + 188 + 3x + x2 = 0 + 188 Combine like terms: -188 + 188 = 0 0 + 3x + x2 = 0 + 188 3x + x2 = 0 + 188 Combine like terms: 0 + 188 = 188 3x + x2 = 188 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 = 188 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 188 + 2.25 Combine like terms: 188 + 2.25 = 190.25 2.25 + 3x + x2 = 190.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 190.25 Calculate the square root of the right side: 13.793114224 Break this problem into two subproblems by setting (x + 1.5) equal to 13.793114224 and -13.793114224.Subproblem 1
x + 1.5 = 13.793114224 Simplifying x + 1.5 = 13.793114224 Reorder the terms: 1.5 + x = 13.793114224 Solving 1.5 + x = 13.793114224 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 = 13.793114224 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 13.793114224 + -1.5 x = 13.793114224 + -1.5 Combine like terms: 13.793114224 + -1.5 = 12.293114224 x = 12.293114224 Simplifying x = 12.293114224Subproblem 2
x + 1.5 = -13.793114224 Simplifying x + 1.5 = -13.793114224 Reorder the terms: 1.5 + x = -13.793114224 Solving 1.5 + x = -13.793114224 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 = -13.793114224 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -13.793114224 + -1.5 x = -13.793114224 + -1.5 Combine like terms: -13.793114224 + -1.5 = -15.293114224 x = -15.293114224 Simplifying x = -15.293114224Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.293114224, -15.293114224}
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