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Simplifying x2 + 0.02x + -0.9999 = 0 Reorder the terms: -0.9999 + 0.02x + x2 = 0 Solving -0.9999 + 0.02x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.9999' to each side of the equation. -0.9999 + 0.02x + 0.9999 + x2 = 0 + 0.9999 Reorder the terms: -0.9999 + 0.9999 + 0.02x + x2 = 0 + 0.9999 Combine like terms: -0.9999 + 0.9999 = 0.0000 0.0000 + 0.02x + x2 = 0 + 0.9999 0.02x + x2 = 0 + 0.9999 Combine like terms: 0 + 0.9999 = 0.9999 0.02x + x2 = 0.9999 The x term is 0.02x. Take half its coefficient (0.01). Square it (0.0001) and add it to both sides. Add '0.0001' to each side of the equation. 0.02x + 0.0001 + x2 = 0.9999 + 0.0001 Reorder the terms: 0.0001 + 0.02x + x2 = 0.9999 + 0.0001 Combine like terms: 0.9999 + 0.0001 = 1 0.0001 + 0.02x + x2 = 1 Factor a perfect square on the left side: (x + 0.01)(x + 0.01) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + 0.01) equal to 1 and -1.Subproblem 1
x + 0.01 = 1 Simplifying x + 0.01 = 1 Reorder the terms: 0.01 + x = 1 Solving 0.01 + x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01' to each side of the equation. 0.01 + -0.01 + x = 1 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + x = 1 + -0.01 x = 1 + -0.01 Combine like terms: 1 + -0.01 = 0.99 x = 0.99 Simplifying x = 0.99Subproblem 2
x + 0.01 = -1 Simplifying x + 0.01 = -1 Reorder the terms: 0.01 + x = -1 Solving 0.01 + x = -1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01' to each side of the equation. 0.01 + -0.01 + x = -1 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + x = -1 + -0.01 x = -1 + -0.01 Combine like terms: -1 + -0.01 = -1.01 x = -1.01 Simplifying x = -1.01Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.99, -1.01}
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