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Simplifying x2 + -2.05x + 1 = 0 Reorder the terms: 1 + -2.05x + x2 = 0 Solving 1 + -2.05x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.05x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.05x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.05x + x2 = 0 + -1 -2.05x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.05x + x2 = -1 The x term is -2.05x. Take half its coefficient (-1.025). Square it (1.050625) and add it to both sides. Add '1.050625' to each side of the equation. -2.05x + 1.050625 + x2 = -1 + 1.050625 Reorder the terms: 1.050625 + -2.05x + x2 = -1 + 1.050625 Combine like terms: -1 + 1.050625 = 0.050625 1.050625 + -2.05x + x2 = 0.050625 Factor a perfect square on the left side: (x + -1.025)(x + -1.025) = 0.050625 Calculate the square root of the right side: 0.225 Break this problem into two subproblems by setting (x + -1.025) equal to 0.225 and -0.225.Subproblem 1
x + -1.025 = 0.225 Simplifying x + -1.025 = 0.225 Reorder the terms: -1.025 + x = 0.225 Solving -1.025 + x = 0.225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.025' to each side of the equation. -1.025 + 1.025 + x = 0.225 + 1.025 Combine like terms: -1.025 + 1.025 = 0.000 0.000 + x = 0.225 + 1.025 x = 0.225 + 1.025 Combine like terms: 0.225 + 1.025 = 1.25 x = 1.25 Simplifying x = 1.25Subproblem 2
x + -1.025 = -0.225 Simplifying x + -1.025 = -0.225 Reorder the terms: -1.025 + x = -0.225 Solving -1.025 + x = -0.225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.025' to each side of the equation. -1.025 + 1.025 + x = -0.225 + 1.025 Combine like terms: -1.025 + 1.025 = 0.000 0.000 + x = -0.225 + 1.025 x = -0.225 + 1.025 Combine like terms: -0.225 + 1.025 = 0.8 x = 0.8 Simplifying x = 0.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.25, 0.8}
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