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Simplifying 1 = (0.02 * 0.02) + (0.02x) + (x * x) Multiply 0.02 * 0.02 1 = (0.0004) + (0.02x) + (x * x) 1 = 0.0004 + (0.02x) + (x * x) Multiply x * x 1 = 0.0004 + (0.02x) + (x2) 1 = 0.0004 + (0.02x) + x2 Solving 1 = 0.0004 + (0.02x) + x2 Solving for variable 'x'. Combine like terms: 1 + -0.0004 = 0.9996 0.9996 + (-0.02x) + -1x2 = 0.0004 + (0.02x) + x2 + -0.0004 + (-0.02x) + -1x2 Reorder the terms: 0.9996 + (-0.02x) + -1x2 = 0.0004 + -0.0004 + (0.02x) + (-0.02x) + x2 + -1x2 Combine like terms: 0.0004 + -0.0004 = 0.0000 0.9996 + (-0.02x) + -1x2 = 0.0000 + (0.02x) + (-0.02x) + x2 + -1x2 0.9996 + (-0.02x) + -1x2 = (0.02x) + (-0.02x) + x2 + -1x2 Combine like terms: (0.02x) + (-0.02x) = 0.00 0.9996 + (-0.02x) + -1x2 = 0.00 + x2 + -1x2 0.9996 + (-0.02x) + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.9996 + (-0.02x) + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.9996 + (0.02x) + x2 = 0 Move the constant term to the right: Add '0.9996' to each side of the equation. -0.9996 + (0.02x) + 0.9996 + x2 = 0 + 0.9996 Reorder the terms: -0.9996 + 0.9996 + (0.02x) + x2 = 0 + 0.9996 Combine like terms: -0.9996 + 0.9996 = 0.0000 0.0000 + (0.02x) + x2 = 0 + 0.9996 (0.02x) + x2 = 0 + 0.9996 Combine like terms: 0 + 0.9996 = 0.9996 (0.02x) + x2 = 0.9996 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 = 0.9996 + 0.0001 Reorder the terms: 0.0001 + (0.02x) + x2 = 0.9996 + 0.0001 Combine like terms: 0.9996 + 0.0001 = 0.9997 0.0001 + (0.02x) + x2 = 0.9997 Factor a perfect square on the left side: (x + 0.01)(x + 0.01) = 0.9997 Calculate the square root of the right side: 0.999849989 Break this problem into two subproblems by setting (x + 0.01) equal to 0.999849989 and -0.999849989.Subproblem 1
x + 0.01 = 0.999849989 Simplifying x + 0.01 = 0.999849989 Reorder the terms: 0.01 + x = 0.999849989 Solving 0.01 + x = 0.999849989 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 = 0.999849989 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + x = 0.999849989 + -0.01 x = 0.999849989 + -0.01 Combine like terms: 0.999849989 + -0.01 = 0.989849989 x = 0.989849989 Simplifying x = 0.989849989Subproblem 2
x + 0.01 = -0.999849989 Simplifying x + 0.01 = -0.999849989 Reorder the terms: 0.01 + x = -0.999849989 Solving 0.01 + x = -0.999849989 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 = -0.999849989 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + x = -0.999849989 + -0.01 x = -0.999849989 + -0.01 Combine like terms: -0.999849989 + -0.01 = -1.009849989 x = -1.009849989 Simplifying x = -1.009849989Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.989849989, -1.009849989}
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