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Simplifying x2 + -2x + -33.4 = 0 Reorder the terms: -33.4 + -2x + x2 = 0 Solving -33.4 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '33.4' to each side of the equation. -33.4 + -2x + 33.4 + x2 = 0 + 33.4 Reorder the terms: -33.4 + 33.4 + -2x + x2 = 0 + 33.4 Combine like terms: -33.4 + 33.4 = 0.0 0.0 + -2x + x2 = 0 + 33.4 -2x + x2 = 0 + 33.4 Combine like terms: 0 + 33.4 = 33.4 -2x + x2 = 33.4 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 33.4 + 1 Reorder the terms: 1 + -2x + x2 = 33.4 + 1 Combine like terms: 33.4 + 1 = 34.4 1 + -2x + x2 = 34.4 Factor a perfect square on the left side: (x + -1)(x + -1) = 34.4 Calculate the square root of the right side: 5.865151319 Break this problem into two subproblems by setting (x + -1) equal to 5.865151319 and -5.865151319.Subproblem 1
x + -1 = 5.865151319 Simplifying x + -1 = 5.865151319 Reorder the terms: -1 + x = 5.865151319 Solving -1 + x = 5.865151319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 5.865151319 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.865151319 + 1 x = 5.865151319 + 1 Combine like terms: 5.865151319 + 1 = 6.865151319 x = 6.865151319 Simplifying x = 6.865151319Subproblem 2
x + -1 = -5.865151319 Simplifying x + -1 = -5.865151319 Reorder the terms: -1 + x = -5.865151319 Solving -1 + x = -5.865151319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -5.865151319 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.865151319 + 1 x = -5.865151319 + 1 Combine like terms: -5.865151319 + 1 = -4.865151319 x = -4.865151319 Simplifying x = -4.865151319Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.865151319, -4.865151319}
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