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Simplifying x2 + -3x + -13.3 = 0 Reorder the terms: -13.3 + -3x + x2 = 0 Solving -13.3 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '13.3' to each side of the equation. -13.3 + -3x + 13.3 + x2 = 0 + 13.3 Reorder the terms: -13.3 + 13.3 + -3x + x2 = 0 + 13.3 Combine like terms: -13.3 + 13.3 = 0.0 0.0 + -3x + x2 = 0 + 13.3 -3x + x2 = 0 + 13.3 Combine like terms: 0 + 13.3 = 13.3 -3x + x2 = 13.3 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 = 13.3 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 13.3 + 2.25 Combine like terms: 13.3 + 2.25 = 15.55 2.25 + -3x + x2 = 15.55 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 15.55 Calculate the square root of the right side: 3.943348831 Break this problem into two subproblems by setting (x + -1.5) equal to 3.943348831 and -3.943348831.Subproblem 1
x + -1.5 = 3.943348831 Simplifying x + -1.5 = 3.943348831 Reorder the terms: -1.5 + x = 3.943348831 Solving -1.5 + x = 3.943348831 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 = 3.943348831 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.943348831 + 1.5 x = 3.943348831 + 1.5 Combine like terms: 3.943348831 + 1.5 = 5.443348831 x = 5.443348831 Simplifying x = 5.443348831Subproblem 2
x + -1.5 = -3.943348831 Simplifying x + -1.5 = -3.943348831 Reorder the terms: -1.5 + x = -3.943348831 Solving -1.5 + x = -3.943348831 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 = -3.943348831 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.943348831 + 1.5 x = -3.943348831 + 1.5 Combine like terms: -3.943348831 + 1.5 = -2.443348831 x = -2.443348831 Simplifying x = -2.443348831Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.443348831, -2.443348831}
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