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Simplifying x2 + -0.85x + -0.85 = 0 Reorder the terms: -0.85 + -0.85x + x2 = 0 Solving -0.85 + -0.85x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.85' to each side of the equation. -0.85 + -0.85x + 0.85 + x2 = 0 + 0.85 Reorder the terms: -0.85 + 0.85 + -0.85x + x2 = 0 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + -0.85x + x2 = 0 + 0.85 -0.85x + x2 = 0 + 0.85 Combine like terms: 0 + 0.85 = 0.85 -0.85x + x2 = 0.85 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 = 0.85 + 0.180625 Reorder the terms: 0.180625 + -0.85x + x2 = 0.85 + 0.180625 Combine like terms: 0.85 + 0.180625 = 1.030625 0.180625 + -0.85x + x2 = 1.030625 Factor a perfect square on the left side: (x + -0.425)(x + -0.425) = 1.030625 Calculate the square root of the right side: 1.015197025 Break this problem into two subproblems by setting (x + -0.425) equal to 1.015197025 and -1.015197025.Subproblem 1
x + -0.425 = 1.015197025 Simplifying x + -0.425 = 1.015197025 Reorder the terms: -0.425 + x = 1.015197025 Solving -0.425 + x = 1.015197025 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 = 1.015197025 + 0.425 Combine like terms: -0.425 + 0.425 = 0.000 0.000 + x = 1.015197025 + 0.425 x = 1.015197025 + 0.425 Combine like terms: 1.015197025 + 0.425 = 1.440197025 x = 1.440197025 Simplifying x = 1.440197025Subproblem 2
x + -0.425 = -1.015197025 Simplifying x + -0.425 = -1.015197025 Reorder the terms: -0.425 + x = -1.015197025 Solving -0.425 + x = -1.015197025 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 = -1.015197025 + 0.425 Combine like terms: -0.425 + 0.425 = 0.000 0.000 + x = -1.015197025 + 0.425 x = -1.015197025 + 0.425 Combine like terms: -1.015197025 + 0.425 = -0.590197025 x = -0.590197025 Simplifying x = -0.590197025Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.440197025, -0.590197025}
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