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Simplifying x2 + 0.0064x + -0.000832 = 0 Reorder the terms: -0.000832 + 0.0064x + x2 = 0 Solving -0.000832 + 0.0064x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.000832' to each side of the equation. -0.000832 + 0.0064x + 0.000832 + x2 = 0 + 0.000832 Reorder the terms: -0.000832 + 0.000832 + 0.0064x + x2 = 0 + 0.000832 Combine like terms: -0.000832 + 0.000832 = 0.000000 0.000000 + 0.0064x + x2 = 0 + 0.000832 0.0064x + x2 = 0 + 0.000832 Combine like terms: 0 + 0.000832 = 0.000832 0.0064x + x2 = 0.000832 The x term is 0.0064x. Take half its coefficient (0.0032). Square it (0.00001024) and add it to both sides. Add '0.00001024' to each side of the equation. 0.0064x + 0.00001024 + x2 = 0.000832 + 0.00001024 Reorder the terms: 0.00001024 + 0.0064x + x2 = 0.000832 + 0.00001024 Combine like terms: 0.000832 + 0.00001024 = 0.00084224 0.00001024 + 0.0064x + x2 = 0.00084224 Factor a perfect square on the left side: (x + 0.0032)(x + 0.0032) = 0.00084224 Calculate the square root of the right side: 0.029021371 Break this problem into two subproblems by setting (x + 0.0032) equal to 0.029021371 and -0.029021371.Subproblem 1
x + 0.0032 = 0.029021371 Simplifying x + 0.0032 = 0.029021371 Reorder the terms: 0.0032 + x = 0.029021371 Solving 0.0032 + x = 0.029021371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0032' to each side of the equation. 0.0032 + -0.0032 + x = 0.029021371 + -0.0032 Combine like terms: 0.0032 + -0.0032 = 0.0000 0.0000 + x = 0.029021371 + -0.0032 x = 0.029021371 + -0.0032 Combine like terms: 0.029021371 + -0.0032 = 0.025821371 x = 0.025821371 Simplifying x = 0.025821371Subproblem 2
x + 0.0032 = -0.029021371 Simplifying x + 0.0032 = -0.029021371 Reorder the terms: 0.0032 + x = -0.029021371 Solving 0.0032 + x = -0.029021371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0032' to each side of the equation. 0.0032 + -0.0032 + x = -0.029021371 + -0.0032 Combine like terms: 0.0032 + -0.0032 = 0.0000 0.0000 + x = -0.029021371 + -0.0032 x = -0.029021371 + -0.0032 Combine like terms: -0.029021371 + -0.0032 = -0.032221371 x = -0.032221371 Simplifying x = -0.032221371Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.025821371, -0.032221371}
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