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Simplifying 44 + -1(3x + 4) = 2(x + 5) * x Reorder the terms: 44 + -1(4 + 3x) = 2(x + 5) * x 44 + (4 * -1 + 3x * -1) = 2(x + 5) * x 44 + (-4 + -3x) = 2(x + 5) * x Combine like terms: 44 + -4 = 40 40 + -3x = 2(x + 5) * x Reorder the terms: 40 + -3x = 2(5 + x) * x Reorder the terms for easier multiplication: 40 + -3x = 2x(5 + x) 40 + -3x = (5 * 2x + x * 2x) 40 + -3x = (10x + 2x2) Solving 40 + -3x = 10x + 2x2 Solving for variable 'x'. Combine like terms: -3x + -10x = -13x 40 + -13x + -2x2 = 10x + 2x2 + -10x + -2x2 Reorder the terms: 40 + -13x + -2x2 = 10x + -10x + 2x2 + -2x2 Combine like terms: 10x + -10x = 0 40 + -13x + -2x2 = 0 + 2x2 + -2x2 40 + -13x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 40 + -13x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -20 + 6.5x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 6.5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 6.5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 6.5x + x2 = 0 + 20 6.5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 6.5x + x2 = 20 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 20 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 20 + 10.5625 Combine like terms: 20 + 10.5625 = 30.5625 10.5625 + 6.5x + x2 = 30.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 30.5625 Calculate the square root of the right side: 5.528336097 Break this problem into two subproblems by setting (x + 3.25) equal to 5.528336097 and -5.528336097.Subproblem 1
x + 3.25 = 5.528336097 Simplifying x + 3.25 = 5.528336097 Reorder the terms: 3.25 + x = 5.528336097 Solving 3.25 + x = 5.528336097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 5.528336097 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 5.528336097 + -3.25 x = 5.528336097 + -3.25 Combine like terms: 5.528336097 + -3.25 = 2.278336097 x = 2.278336097 Simplifying x = 2.278336097Subproblem 2
x + 3.25 = -5.528336097 Simplifying x + 3.25 = -5.528336097 Reorder the terms: 3.25 + x = -5.528336097 Solving 3.25 + x = -5.528336097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -5.528336097 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -5.528336097 + -3.25 x = -5.528336097 + -3.25 Combine like terms: -5.528336097 + -3.25 = -8.778336097 x = -8.778336097 Simplifying x = -8.778336097Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.278336097, -8.778336097}
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