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Simplifying 4x2 + 0.2x = 0.06 Reorder the terms: 0.2x + 4x2 = 0.06 Solving 0.2x + 4x2 = 0.06 Solving for variable 'x'. Reorder the terms: -0.06 + 0.2x + 4x2 = 0.06 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 -0.06 + 0.2x + 4x2 = 0.00 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.015 + 0.05x + x2 = 0.00 Move the constant term to the right: Add '0.015' to each side of the equation. -0.015 + 0.05x + 0.015 + x2 = 0.00 + 0.015 Reorder the terms: -0.015 + 0.015 + 0.05x + x2 = 0.00 + 0.015 Combine like terms: -0.015 + 0.015 = 0.000 0.000 + 0.05x + x2 = 0.00 + 0.015 0.05x + x2 = 0.00 + 0.015 Combine like terms: 0.00 + 0.015 = 0.015 0.05x + x2 = 0.015 The x term is 0.05x. Take half its coefficient (0.025). Square it (0.000625) and add it to both sides. Add '0.000625' to each side of the equation. 0.05x + 0.000625 + x2 = 0.015 + 0.000625 Reorder the terms: 0.000625 + 0.05x + x2 = 0.015 + 0.000625 Combine like terms: 0.015 + 0.000625 = 0.015625 0.000625 + 0.05x + x2 = 0.015625 Factor a perfect square on the left side: (x + 0.025)(x + 0.025) = 0.015625 Calculate the square root of the right side: 0.125 Break this problem into two subproblems by setting (x + 0.025) equal to 0.125 and -0.125.Subproblem 1
x + 0.025 = 0.125 Simplifying x + 0.025 = 0.125 Reorder the terms: 0.025 + x = 0.125 Solving 0.025 + x = 0.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.025' to each side of the equation. 0.025 + -0.025 + x = 0.125 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + x = 0.125 + -0.025 x = 0.125 + -0.025 Combine like terms: 0.125 + -0.025 = 0.1 x = 0.1 Simplifying x = 0.1Subproblem 2
x + 0.025 = -0.125 Simplifying x + 0.025 = -0.125 Reorder the terms: 0.025 + x = -0.125 Solving 0.025 + x = -0.125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.025' to each side of the equation. 0.025 + -0.025 + x = -0.125 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + x = -0.125 + -0.025 x = -0.125 + -0.025 Combine like terms: -0.125 + -0.025 = -0.15 x = -0.15 Simplifying x = -0.15Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1, -0.15}
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