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Simplifying x2 + 5x + 0.01 = 0 Reorder the terms: 0.01 + 5x + x2 = 0 Solving 0.01 + 5x + 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 + 5x + -0.01 + x2 = 0 + -0.01 Reorder the terms: 0.01 + -0.01 + 5x + x2 = 0 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + 5x + x2 = 0 + -0.01 5x + x2 = 0 + -0.01 Combine like terms: 0 + -0.01 = -0.01 5x + x2 = -0.01 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -0.01 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -0.01 + 6.25 Combine like terms: -0.01 + 6.25 = 6.24 6.25 + 5x + x2 = 6.24 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 6.24 Calculate the square root of the right side: 2.497999199 Break this problem into two subproblems by setting (x + 2.5) equal to 2.497999199 and -2.497999199.Subproblem 1
x + 2.5 = 2.497999199 Simplifying x + 2.5 = 2.497999199 Reorder the terms: 2.5 + x = 2.497999199 Solving 2.5 + x = 2.497999199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.497999199 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.497999199 + -2.5 x = 2.497999199 + -2.5 Combine like terms: 2.497999199 + -2.5 = -0.002000801 x = -0.002000801 Simplifying x = -0.002000801Subproblem 2
x + 2.5 = -2.497999199 Simplifying x + 2.5 = -2.497999199 Reorder the terms: 2.5 + x = -2.497999199 Solving 2.5 + x = -2.497999199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.497999199 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.497999199 + -2.5 x = -2.497999199 + -2.5 Combine like terms: -2.497999199 + -2.5 = -4.997999199 x = -4.997999199 Simplifying x = -4.997999199Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.002000801, -4.997999199}
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