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Simplifying x2 + 0.65x = 0.000001 Reorder the terms: 0.65x + x2 = 0.000001 Solving 0.65x + x2 = 0.000001 Solving for variable 'x'. Reorder the terms: -0.000001 + 0.65x + x2 = 0.000001 + -0.000001 Combine like terms: 0.000001 + -0.000001 = 0.000000 -0.000001 + 0.65x + x2 = 0.000000 Begin completing the square. Move the constant term to the right: Add '0.000001' to each side of the equation. -0.000001 + 0.65x + 0.000001 + x2 = 0.000000 + 0.000001 Reorder the terms: -0.000001 + 0.000001 + 0.65x + x2 = 0.000000 + 0.000001 Combine like terms: -0.000001 + 0.000001 = 0.000000 0.000000 + 0.65x + x2 = 0.000000 + 0.000001 0.65x + x2 = 0.000000 + 0.000001 Combine like terms: 0.000000 + 0.000001 = 0.000001 0.65x + x2 = 0.000001 The x term is 0.65x. Take half its coefficient (0.325). Square it (0.105625) and add it to both sides. Add '0.105625' to each side of the equation. 0.65x + 0.105625 + x2 = 0.000001 + 0.105625 Reorder the terms: 0.105625 + 0.65x + x2 = 0.000001 + 0.105625 Combine like terms: 0.000001 + 0.105625 = 0.105626 0.105625 + 0.65x + x2 = 0.105626 Factor a perfect square on the left side: (x + 0.325)(x + 0.325) = 0.105626 Calculate the square root of the right side: 0.325001538 Break this problem into two subproblems by setting (x + 0.325) equal to 0.325001538 and -0.325001538.Subproblem 1
x + 0.325 = 0.325001538 Simplifying x + 0.325 = 0.325001538 Reorder the terms: 0.325 + x = 0.325001538 Solving 0.325 + x = 0.325001538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.325' to each side of the equation. 0.325 + -0.325 + x = 0.325001538 + -0.325 Combine like terms: 0.325 + -0.325 = 0.000 0.000 + x = 0.325001538 + -0.325 x = 0.325001538 + -0.325 Combine like terms: 0.325001538 + -0.325 = 0.000001538 x = 0.000001538 Simplifying x = 0.000001538Subproblem 2
x + 0.325 = -0.325001538 Simplifying x + 0.325 = -0.325001538 Reorder the terms: 0.325 + x = -0.325001538 Solving 0.325 + x = -0.325001538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.325' to each side of the equation. 0.325 + -0.325 + x = -0.325001538 + -0.325 Combine like terms: 0.325 + -0.325 = 0.000 0.000 + x = -0.325001538 + -0.325 x = -0.325001538 + -0.325 Combine like terms: -0.325001538 + -0.325 = -0.650001538 x = -0.650001538 Simplifying x = -0.650001538Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000001538, -0.650001538}
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