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Simplifying x2 + -2.1x + 0.8 = 0 Reorder the terms: 0.8 + -2.1x + x2 = 0 Solving 0.8 + -2.1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -2.1x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -2.1x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -2.1x + x2 = 0 + -0.8 -2.1x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -2.1x + x2 = -0.8 The x term is -2.1x. Take half its coefficient (-1.05). Square it (1.1025) and add it to both sides. Add '1.1025' to each side of the equation. -2.1x + 1.1025 + x2 = -0.8 + 1.1025 Reorder the terms: 1.1025 + -2.1x + x2 = -0.8 + 1.1025 Combine like terms: -0.8 + 1.1025 = 0.3025 1.1025 + -2.1x + x2 = 0.3025 Factor a perfect square on the left side: (x + -1.05)(x + -1.05) = 0.3025 Calculate the square root of the right side: 0.55 Break this problem into two subproblems by setting (x + -1.05) equal to 0.55 and -0.55.Subproblem 1
x + -1.05 = 0.55 Simplifying x + -1.05 = 0.55 Reorder the terms: -1.05 + x = 0.55 Solving -1.05 + x = 0.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x = 0.55 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = 0.55 + 1.05 x = 0.55 + 1.05 Combine like terms: 0.55 + 1.05 = 1.6 x = 1.6 Simplifying x = 1.6Subproblem 2
x + -1.05 = -0.55 Simplifying x + -1.05 = -0.55 Reorder the terms: -1.05 + x = -0.55 Solving -1.05 + x = -0.55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x = -0.55 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = -0.55 + 1.05 x = -0.55 + 1.05 Combine like terms: -0.55 + 1.05 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6, 0.5}
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