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Simplifying x2 + -3x + -105 = 0 Reorder the terms: -105 + -3x + x2 = 0 Solving -105 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '105' to each side of the equation. -105 + -3x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + -3x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + -3x + x2 = 0 + 105 -3x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 -3x + x2 = 105 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 = 105 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 105 + 2.25 Combine like terms: 105 + 2.25 = 107.25 2.25 + -3x + x2 = 107.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 107.25 Calculate the square root of the right side: 10.356157589 Break this problem into two subproblems by setting (x + -1.5) equal to 10.356157589 and -10.356157589.Subproblem 1
x + -1.5 = 10.356157589 Simplifying x + -1.5 = 10.356157589 Reorder the terms: -1.5 + x = 10.356157589 Solving -1.5 + x = 10.356157589 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 = 10.356157589 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 10.356157589 + 1.5 x = 10.356157589 + 1.5 Combine like terms: 10.356157589 + 1.5 = 11.856157589 x = 11.856157589 Simplifying x = 11.856157589Subproblem 2
x + -1.5 = -10.356157589 Simplifying x + -1.5 = -10.356157589 Reorder the terms: -1.5 + x = -10.356157589 Solving -1.5 + x = -10.356157589 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 = -10.356157589 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -10.356157589 + 1.5 x = -10.356157589 + 1.5 Combine like terms: -10.356157589 + 1.5 = -8.856157589 x = -8.856157589 Simplifying x = -8.856157589Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.856157589, -8.856157589}
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