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Simplifying (6x + -3) * x = 50 Reorder the terms: (-3 + 6x) * x = 50 Reorder the terms for easier multiplication: x(-3 + 6x) = 50 (-3 * x + 6x * x) = 50 (-3x + 6x2) = 50 Solving -3x + 6x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + -3x + 6x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + -3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -8.333333333 + -0.5x + x2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + -0.5x + 8.333333333 + x2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + -0.5x + x2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + -0.5x + x2 = 0 + 8.333333333 -0.5x + x2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 -0.5x + x2 = 8.333333333 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 8.333333333 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 8.333333333 + 0.0625 Combine like terms: 8.333333333 + 0.0625 = 8.395833333 0.0625 + -0.5x + x2 = 8.395833333 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 8.395833333 Calculate the square root of the right side: 2.897556442 Break this problem into two subproblems by setting (x + -0.25) equal to 2.897556442 and -2.897556442.Subproblem 1
x + -0.25 = 2.897556442 Simplifying x + -0.25 = 2.897556442 Reorder the terms: -0.25 + x = 2.897556442 Solving -0.25 + x = 2.897556442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.897556442 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.897556442 + 0.25 x = 2.897556442 + 0.25 Combine like terms: 2.897556442 + 0.25 = 3.147556442 x = 3.147556442 Simplifying x = 3.147556442Subproblem 2
x + -0.25 = -2.897556442 Simplifying x + -0.25 = -2.897556442 Reorder the terms: -0.25 + x = -2.897556442 Solving -0.25 + x = -2.897556442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.897556442 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.897556442 + 0.25 x = -2.897556442 + 0.25 Combine like terms: -2.897556442 + 0.25 = -2.647556442 x = -2.647556442 Simplifying x = -2.647556442Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.147556442, -2.647556442}
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