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Simplifying x2 + x + -0.01 = 0 Reorder the terms: -0.01 + x + x2 = 0 Solving -0.01 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.01' to each side of the equation. -0.01 + x + 0.01 + x2 = 0 + 0.01 Reorder the terms: -0.01 + 0.01 + x + x2 = 0 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + x + x2 = 0 + 0.01 x + x2 = 0 + 0.01 Combine like terms: 0 + 0.01 = 0.01 x + x2 = 0.01 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 0.01 + 0.25 Reorder the terms: 0.25 + x + x2 = 0.01 + 0.25 Combine like terms: 0.01 + 0.25 = 0.26 0.25 + x + x2 = 0.26 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.26 Calculate the square root of the right side: 0.509901951 Break this problem into two subproblems by setting (x + 0.5) equal to 0.509901951 and -0.509901951.Subproblem 1
x + 0.5 = 0.509901951 Simplifying x + 0.5 = 0.509901951 Reorder the terms: 0.5 + x = 0.509901951 Solving 0.5 + x = 0.509901951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.509901951 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.509901951 + -0.5 x = 0.509901951 + -0.5 Combine like terms: 0.509901951 + -0.5 = 0.009901951 x = 0.009901951 Simplifying x = 0.009901951Subproblem 2
x + 0.5 = -0.509901951 Simplifying x + 0.5 = -0.509901951 Reorder the terms: 0.5 + x = -0.509901951 Solving 0.5 + x = -0.509901951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.509901951 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.509901951 + -0.5 x = -0.509901951 + -0.5 Combine like terms: -0.509901951 + -0.5 = -1.009901951 x = -1.009901951 Simplifying x = -1.009901951Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.009901951, -1.009901951}
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