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Simplifying (x + 0.06) * x = 159 Reorder the terms: (0.06 + x) * x = 159 Reorder the terms for easier multiplication: x(0.06 + x) = 159 (0.06 * x + x * x) = 159 (0.06x + x2) = 159 Solving 0.06x + x2 = 159 Solving for variable 'x'. Reorder the terms: -159 + 0.06x + x2 = 159 + -159 Combine like terms: 159 + -159 = 0 -159 + 0.06x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '159' to each side of the equation. -159 + 0.06x + 159 + x2 = 0 + 159 Reorder the terms: -159 + 159 + 0.06x + x2 = 0 + 159 Combine like terms: -159 + 159 = 0 0 + 0.06x + x2 = 0 + 159 0.06x + x2 = 0 + 159 Combine like terms: 0 + 159 = 159 0.06x + x2 = 159 The x term is 0.06x. Take half its coefficient (0.03). Square it (0.0009) and add it to both sides. Add '0.0009' to each side of the equation. 0.06x + 0.0009 + x2 = 159 + 0.0009 Reorder the terms: 0.0009 + 0.06x + x2 = 159 + 0.0009 Combine like terms: 159 + 0.0009 = 159.0009 0.0009 + 0.06x + x2 = 159.0009 Factor a perfect square on the left side: (x + 0.03)(x + 0.03) = 159.0009 Calculate the square root of the right side: 12.6095559 Break this problem into two subproblems by setting (x + 0.03) equal to 12.6095559 and -12.6095559.Subproblem 1
x + 0.03 = 12.6095559 Simplifying x + 0.03 = 12.6095559 Reorder the terms: 0.03 + x = 12.6095559 Solving 0.03 + x = 12.6095559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03' to each side of the equation. 0.03 + -0.03 + x = 12.6095559 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 0.00 + x = 12.6095559 + -0.03 x = 12.6095559 + -0.03 Combine like terms: 12.6095559 + -0.03 = 12.5795559 x = 12.5795559 Simplifying x = 12.5795559Subproblem 2
x + 0.03 = -12.6095559 Simplifying x + 0.03 = -12.6095559 Reorder the terms: 0.03 + x = -12.6095559 Solving 0.03 + x = -12.6095559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03' to each side of the equation. 0.03 + -0.03 + x = -12.6095559 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 0.00 + x = -12.6095559 + -0.03 x = -12.6095559 + -0.03 Combine like terms: -12.6095559 + -0.03 = -12.6395559 x = -12.6395559 Simplifying x = -12.6395559Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.5795559, -12.6395559}
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