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Simplifying x2 + -1x + -2.55 = 0 Reorder the terms: -2.55 + -1x + x2 = 0 Solving -2.55 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2.55' to each side of the equation. -2.55 + -1x + 2.55 + x2 = 0 + 2.55 Reorder the terms: -2.55 + 2.55 + -1x + x2 = 0 + 2.55 Combine like terms: -2.55 + 2.55 = 0.00 0.00 + -1x + x2 = 0 + 2.55 -1x + x2 = 0 + 2.55 Combine like terms: 0 + 2.55 = 2.55 -1x + x2 = 2.55 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.55 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.55 + 0.25 Combine like terms: 2.55 + 0.25 = 2.8 0.25 + -1x + x2 = 2.8 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.8 Calculate the square root of the right side: 1.673320053 Break this problem into two subproblems by setting (x + -0.5) equal to 1.673320053 and -1.673320053.Subproblem 1
x + -0.5 = 1.673320053 Simplifying x + -0.5 = 1.673320053 Reorder the terms: -0.5 + x = 1.673320053 Solving -0.5 + x = 1.673320053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.673320053 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.673320053 + 0.5 x = 1.673320053 + 0.5 Combine like terms: 1.673320053 + 0.5 = 2.173320053 x = 2.173320053 Simplifying x = 2.173320053Subproblem 2
x + -0.5 = -1.673320053 Simplifying x + -0.5 = -1.673320053 Reorder the terms: -0.5 + x = -1.673320053 Solving -0.5 + x = -1.673320053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.673320053 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.673320053 + 0.5 x = -1.673320053 + 0.5 Combine like terms: -1.673320053 + 0.5 = -1.173320053 x = -1.173320053 Simplifying x = -1.173320053Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.173320053, -1.173320053}
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