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Simplifying -0.10(44) + 0.35x = 0.05x(x + -16) Multiply -0.10 * 44 -4.4 + 0.35x = 0.05x(x + -16) Reorder the terms: -4.4 + 0.35x = 0.05x(-16 + x) -4.4 + 0.35x = (-16 * 0.05x + x * 0.05x) -4.4 + 0.35x = (-0.8x + 0.05x2) Solving -4.4 + 0.35x = -0.8x + 0.05x2 Solving for variable 'x'. Combine like terms: 0.35x + 0.8x = 1.15x -4.4 + 1.15x + -0.05x2 = -0.8x + 0.05x2 + 0.8x + -0.05x2 Reorder the terms: -4.4 + 1.15x + -0.05x2 = -0.8x + 0.8x + 0.05x2 + -0.05x2 Combine like terms: -0.8x + 0.8x = 0.0 -4.4 + 1.15x + -0.05x2 = 0.0 + 0.05x2 + -0.05x2 -4.4 + 1.15x + -0.05x2 = 0.05x2 + -0.05x2 Combine like terms: 0.05x2 + -0.05x2 = 0.00 -4.4 + 1.15x + -0.05x2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. 88 + -23x + x2 = 0 Move the constant term to the right: Add '-88' to each side of the equation. 88 + -23x + -88 + x2 = 0 + -88 Reorder the terms: 88 + -88 + -23x + x2 = 0 + -88 Combine like terms: 88 + -88 = 0 0 + -23x + x2 = 0 + -88 -23x + x2 = 0 + -88 Combine like terms: 0 + -88 = -88 -23x + x2 = -88 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = -88 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -88 + 132.25 Combine like terms: -88 + 132.25 = 44.25 132.25 + -23x + x2 = 44.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + -11.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + -11.5 = 6.652067348 Simplifying x + -11.5 = 6.652067348 Reorder the terms: -11.5 + x = 6.652067348 Solving -11.5 + x = 6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 6.652067348 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 6.652067348 + 11.5 x = 6.652067348 + 11.5 Combine like terms: 6.652067348 + 11.5 = 18.152067348 x = 18.152067348 Simplifying x = 18.152067348Subproblem 2
x + -11.5 = -6.652067348 Simplifying x + -11.5 = -6.652067348 Reorder the terms: -11.5 + x = -6.652067348 Solving -11.5 + x = -6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -6.652067348 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -6.652067348 + 11.5 x = -6.652067348 + 11.5 Combine like terms: -6.652067348 + 11.5 = 4.847932652 x = 4.847932652 Simplifying x = 4.847932652Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.152067348, 4.847932652}
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