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Simplifying x2 + -3x + -190 = 0 Reorder the terms: -190 + -3x + x2 = 0 Solving -190 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '190' to each side of the equation. -190 + -3x + 190 + x2 = 0 + 190 Reorder the terms: -190 + 190 + -3x + x2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + -3x + x2 = 0 + 190 -3x + x2 = 0 + 190 Combine like terms: 0 + 190 = 190 -3x + x2 = 190 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 = 190 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 190 + 2.25 Combine like terms: 190 + 2.25 = 192.25 2.25 + -3x + x2 = 192.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 192.25 Calculate the square root of the right side: 13.865424624 Break this problem into two subproblems by setting (x + -1.5) equal to 13.865424624 and -13.865424624.Subproblem 1
x + -1.5 = 13.865424624 Simplifying x + -1.5 = 13.865424624 Reorder the terms: -1.5 + x = 13.865424624 Solving -1.5 + x = 13.865424624 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 = 13.865424624 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 13.865424624 + 1.5 x = 13.865424624 + 1.5 Combine like terms: 13.865424624 + 1.5 = 15.365424624 x = 15.365424624 Simplifying x = 15.365424624Subproblem 2
x + -1.5 = -13.865424624 Simplifying x + -1.5 = -13.865424624 Reorder the terms: -1.5 + x = -13.865424624 Solving -1.5 + x = -13.865424624 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 = -13.865424624 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -13.865424624 + 1.5 x = -13.865424624 + 1.5 Combine like terms: -13.865424624 + 1.5 = -12.365424624 x = -12.365424624 Simplifying x = -12.365424624Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.365424624, -12.365424624}
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