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Simplifying x(x + 0.07) = 0.026 Reorder the terms: x(0.07 + x) = 0.026 (0.07 * x + x * x) = 0.026 (0.07x + x2) = 0.026 Solving 0.07x + x2 = 0.026 Solving for variable 'x'. Reorder the terms: -0.026 + 0.07x + x2 = 0.026 + -0.026 Combine like terms: 0.026 + -0.026 = 0.000 -0.026 + 0.07x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '0.026' to each side of the equation. -0.026 + 0.07x + 0.026 + x2 = 0.000 + 0.026 Reorder the terms: -0.026 + 0.026 + 0.07x + x2 = 0.000 + 0.026 Combine like terms: -0.026 + 0.026 = 0.000 0.000 + 0.07x + x2 = 0.000 + 0.026 0.07x + x2 = 0.000 + 0.026 Combine like terms: 0.000 + 0.026 = 0.026 0.07x + x2 = 0.026 The x term is 0.07x. Take half its coefficient (0.035). Square it (0.001225) and add it to both sides. Add '0.001225' to each side of the equation. 0.07x + 0.001225 + x2 = 0.026 + 0.001225 Reorder the terms: 0.001225 + 0.07x + x2 = 0.026 + 0.001225 Combine like terms: 0.026 + 0.001225 = 0.027225 0.001225 + 0.07x + x2 = 0.027225 Factor a perfect square on the left side: (x + 0.035)(x + 0.035) = 0.027225 Calculate the square root of the right side: 0.165 Break this problem into two subproblems by setting (x + 0.035) equal to 0.165 and -0.165.Subproblem 1
x + 0.035 = 0.165 Simplifying x + 0.035 = 0.165 Reorder the terms: 0.035 + x = 0.165 Solving 0.035 + x = 0.165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.035' to each side of the equation. 0.035 + -0.035 + x = 0.165 + -0.035 Combine like terms: 0.035 + -0.035 = 0.000 0.000 + x = 0.165 + -0.035 x = 0.165 + -0.035 Combine like terms: 0.165 + -0.035 = 0.13 x = 0.13 Simplifying x = 0.13Subproblem 2
x + 0.035 = -0.165 Simplifying x + 0.035 = -0.165 Reorder the terms: 0.035 + x = -0.165 Solving 0.035 + x = -0.165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.035' to each side of the equation. 0.035 + -0.035 + x = -0.165 + -0.035 Combine like terms: 0.035 + -0.035 = 0.000 0.000 + x = -0.165 + -0.035 x = -0.165 + -0.035 Combine like terms: -0.165 + -0.035 = -0.2 x = -0.2 Simplifying x = -0.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.13, -0.2}
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