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Simplifying 0.00869(0.147 + -1x) = x2 (0.147 * 0.00869 + -1x * 0.00869) = x2 (0.00127743 + -0.00869x) = x2 Solving 0.00127743 + -0.00869x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.00127743 + -0.00869x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.00127743 + 0.00869x + x2 = 0 Move the constant term to the right: Add '0.00127743' to each side of the equation. -0.00127743 + 0.00869x + 0.00127743 + x2 = 0 + 0.00127743 Reorder the terms: -0.00127743 + 0.00127743 + 0.00869x + x2 = 0 + 0.00127743 Combine like terms: -0.00127743 + 0.00127743 = 0.00000000 0.00000000 + 0.00869x + x2 = 0 + 0.00127743 0.00869x + x2 = 0 + 0.00127743 Combine like terms: 0 + 0.00127743 = 0.00127743 0.00869x + x2 = 0.00127743 The x term is 0.00869x. Take half its coefficient (0.004345). Square it (0.000018879025) and add it to both sides. Add '0.000018879025' to each side of the equation. 0.00869x + 0.000018879025 + x2 = 0.00127743 + 0.000018879025 Reorder the terms: 0.000018879025 + 0.00869x + x2 = 0.00127743 + 0.000018879025 Combine like terms: 0.00127743 + 0.000018879025 = 0.001296309025 0.000018879025 + 0.00869x + x2 = 0.001296309025 Factor a perfect square on the left side: (x + 0.004345)(x + 0.004345) = 0.001296309025 Calculate the square root of the right side: 0.036004292 Break this problem into two subproblems by setting (x + 0.004345) equal to 0.036004292 and -0.036004292.Subproblem 1
x + 0.004345 = 0.036004292 Simplifying x + 0.004345 = 0.036004292 Reorder the terms: 0.004345 + x = 0.036004292 Solving 0.004345 + x = 0.036004292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.004345' to each side of the equation. 0.004345 + -0.004345 + x = 0.036004292 + -0.004345 Combine like terms: 0.004345 + -0.004345 = 0.000000 0.000000 + x = 0.036004292 + -0.004345 x = 0.036004292 + -0.004345 Combine like terms: 0.036004292 + -0.004345 = 0.031659292 x = 0.031659292 Simplifying x = 0.031659292Subproblem 2
x + 0.004345 = -0.036004292 Simplifying x + 0.004345 = -0.036004292 Reorder the terms: 0.004345 + x = -0.036004292 Solving 0.004345 + x = -0.036004292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.004345' to each side of the equation. 0.004345 + -0.004345 + x = -0.036004292 + -0.004345 Combine like terms: 0.004345 + -0.004345 = 0.000000 0.000000 + x = -0.036004292 + -0.004345 x = -0.036004292 + -0.004345 Combine like terms: -0.036004292 + -0.004345 = -0.040349292 x = -0.040349292 Simplifying x = -0.040349292Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.031659292, -0.040349292}
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