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Simplifying x2 + -2x + -0.51 = 0 Reorder the terms: -0.51 + -2x + x2 = 0 Solving -0.51 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.51' to each side of the equation. -0.51 + -2x + 0.51 + x2 = 0 + 0.51 Reorder the terms: -0.51 + 0.51 + -2x + x2 = 0 + 0.51 Combine like terms: -0.51 + 0.51 = 0.00 0.00 + -2x + x2 = 0 + 0.51 -2x + x2 = 0 + 0.51 Combine like terms: 0 + 0.51 = 0.51 -2x + x2 = 0.51 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 = 0.51 + 1 Reorder the terms: 1 + -2x + x2 = 0.51 + 1 Combine like terms: 0.51 + 1 = 1.51 1 + -2x + x2 = 1.51 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.51 Calculate the square root of the right side: 1.228820573 Break this problem into two subproblems by setting (x + -1) equal to 1.228820573 and -1.228820573.Subproblem 1
x + -1 = 1.228820573 Simplifying x + -1 = 1.228820573 Reorder the terms: -1 + x = 1.228820573 Solving -1 + x = 1.228820573 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 = 1.228820573 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.228820573 + 1 x = 1.228820573 + 1 Combine like terms: 1.228820573 + 1 = 2.228820573 x = 2.228820573 Simplifying x = 2.228820573Subproblem 2
x + -1 = -1.228820573 Simplifying x + -1 = -1.228820573 Reorder the terms: -1 + x = -1.228820573 Solving -1 + x = -1.228820573 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 = -1.228820573 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.228820573 + 1 x = -1.228820573 + 1 Combine like terms: -1.228820573 + 1 = -0.228820573 x = -0.228820573 Simplifying x = -0.228820573Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.228820573, -0.228820573}
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