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Simplifying x2 + -0.85x + 0.04 = 0 Reorder the terms: 0.04 + -0.85x + x2 = 0 Solving 0.04 + -0.85x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + -0.85x + -0.04 + x2 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + -0.85x + x2 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + -0.85x + x2 = 0 + -0.04 -0.85x + x2 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 -0.85x + x2 = -0.04 The x term is -0.85x. Take half its coefficient (-0.425). Square it (0.180625) and add it to both sides. Add '0.180625' to each side of the equation. -0.85x + 0.180625 + x2 = -0.04 + 0.180625 Reorder the terms: 0.180625 + -0.85x + x2 = -0.04 + 0.180625 Combine like terms: -0.04 + 0.180625 = 0.140625 0.180625 + -0.85x + x2 = 0.140625 Factor a perfect square on the left side: (x + -0.425)(x + -0.425) = 0.140625 Calculate the square root of the right side: 0.375 Break this problem into two subproblems by setting (x + -0.425) equal to 0.375 and -0.375.Subproblem 1
x + -0.425 = 0.375 Simplifying x + -0.425 = 0.375 Reorder the terms: -0.425 + x = 0.375 Solving -0.425 + x = 0.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.425' to each side of the equation. -0.425 + 0.425 + x = 0.375 + 0.425 Combine like terms: -0.425 + 0.425 = 0.000 0.000 + x = 0.375 + 0.425 x = 0.375 + 0.425 Combine like terms: 0.375 + 0.425 = 0.8 x = 0.8 Simplifying x = 0.8Subproblem 2
x + -0.425 = -0.375 Simplifying x + -0.425 = -0.375 Reorder the terms: -0.425 + x = -0.375 Solving -0.425 + x = -0.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.425' to each side of the equation. -0.425 + 0.425 + x = -0.375 + 0.425 Combine like terms: -0.425 + 0.425 = 0.000 0.000 + x = -0.375 + 0.425 x = -0.375 + 0.425 Combine like terms: -0.375 + 0.425 = 0.05 x = 0.05 Simplifying x = 0.05Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8, 0.05}
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