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Simplifying 44 = x(2x + -1.5) Reorder the terms: 44 = x(-1.5 + 2x) 44 = (-1.5 * x + 2x * x) 44 = (-1.5x + 2x2) Solving 44 = -1.5x + 2x2 Solving for variable 'x'. Reorder the terms: 44 + 1.5x + -2x2 = -1.5x + 1.5x + 2x2 + -2x2 Combine like terms: -1.5x + 1.5x = 0.0 44 + 1.5x + -2x2 = 0.0 + 2x2 + -2x2 44 + 1.5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 44 + 1.5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -22 + -0.75x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + -0.75x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -0.75x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -0.75x + x2 = 0 + 22 -0.75x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -0.75x + x2 = 22 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 22 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 22 + 0.140625 Combine like terms: 22 + 0.140625 = 22.140625 0.140625 + -0.75x + x2 = 22.140625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 22.140625 Calculate the square root of the right side: 4.705382556 Break this problem into two subproblems by setting (x + -0.375) equal to 4.705382556 and -4.705382556.Subproblem 1
x + -0.375 = 4.705382556 Simplifying x + -0.375 = 4.705382556 Reorder the terms: -0.375 + x = 4.705382556 Solving -0.375 + x = 4.705382556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 4.705382556 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 4.705382556 + 0.375 x = 4.705382556 + 0.375 Combine like terms: 4.705382556 + 0.375 = 5.080382556 x = 5.080382556 Simplifying x = 5.080382556Subproblem 2
x + -0.375 = -4.705382556 Simplifying x + -0.375 = -4.705382556 Reorder the terms: -0.375 + x = -4.705382556 Solving -0.375 + x = -4.705382556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -4.705382556 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -4.705382556 + 0.375 x = -4.705382556 + 0.375 Combine like terms: -4.705382556 + 0.375 = -4.330382556 x = -4.330382556 Simplifying x = -4.330382556Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.080382556, -4.330382556}
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