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Simplifying (5x + 0.2)(5x + 0.2) = 0 Reorder the terms: (0.2 + 5x)(5x + 0.2) = 0 Reorder the terms: (0.2 + 5x)(0.2 + 5x) = 0 Multiply (0.2 + 5x) * (0.2 + 5x) (0.2(0.2 + 5x) + 5x * (0.2 + 5x)) = 0 ((0.2 * 0.2 + 5x * 0.2) + 5x * (0.2 + 5x)) = 0 ((0.04 + 1x) + 5x * (0.2 + 5x)) = 0 (0.04 + 1x + (0.2 * 5x + 5x * 5x)) = 0 (0.04 + 1x + (1x + 25x2)) = 0 Combine like terms: 1x + 1x = 2x (0.04 + 2x + 25x2) = 0 Solving 0.04 + 2x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.0016 + 0.08x + x2 = 0 Move the constant term to the right: Add '-0.0016' to each side of the equation. 0.0016 + 0.08x + -0.0016 + x2 = 0 + -0.0016 Reorder the terms: 0.0016 + -0.0016 + 0.08x + x2 = 0 + -0.0016 Combine like terms: 0.0016 + -0.0016 = 0.0000 0.0000 + 0.08x + x2 = 0 + -0.0016 0.08x + x2 = 0 + -0.0016 Combine like terms: 0 + -0.0016 = -0.0016 0.08x + x2 = -0.0016 The x term is 0.08x. Take half its coefficient (0.04). Square it (0.0016) and add it to both sides. Add '0.0016' to each side of the equation. 0.08x + 0.0016 + x2 = -0.0016 + 0.0016 Reorder the terms: 0.0016 + 0.08x + x2 = -0.0016 + 0.0016 Combine like terms: -0.0016 + 0.0016 = 0.0000 0.0016 + 0.08x + x2 = 0.0000 Factor a perfect square on the left side: (x + 0.04)(x + 0.04) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + 0.04) equal to 0.0000 and 0.0000.Subproblem 1
x + 0.04 = 0.0000 Simplifying x + 0.04 = 0.0000 Reorder the terms: 0.04 + x = 0.0000 Solving 0.04 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04' to each side of the equation. 0.04 + -0.04 + x = 0.0000 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + x = 0.0000 + -0.04 x = 0.0000 + -0.04 Combine like terms: 0.0000 + -0.04 = -0.04 x = -0.04 Simplifying x = -0.04Subproblem 2
x + 0.04 = 0.0000 Simplifying x + 0.04 = 0.0000 Reorder the terms: 0.04 + x = 0.0000 Solving 0.04 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04' to each side of the equation. 0.04 + -0.04 + x = 0.0000 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + x = 0.0000 + -0.04 x = 0.0000 + -0.04 Combine like terms: 0.0000 + -0.04 = -0.04 x = -0.04 Simplifying x = -0.04Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.04, -0.04}
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