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Simplifying 44 + -1(5x + 6) = 2(x + 7) * x Reorder the terms: 44 + -1(6 + 5x) = 2(x + 7) * x 44 + (6 * -1 + 5x * -1) = 2(x + 7) * x 44 + (-6 + -5x) = 2(x + 7) * x Combine like terms: 44 + -6 = 38 38 + -5x = 2(x + 7) * x Reorder the terms: 38 + -5x = 2(7 + x) * x Reorder the terms for easier multiplication: 38 + -5x = 2x(7 + x) 38 + -5x = (7 * 2x + x * 2x) 38 + -5x = (14x + 2x2) Solving 38 + -5x = 14x + 2x2 Solving for variable 'x'. Combine like terms: -5x + -14x = -19x 38 + -19x + -2x2 = 14x + 2x2 + -14x + -2x2 Reorder the terms: 38 + -19x + -2x2 = 14x + -14x + 2x2 + -2x2 Combine like terms: 14x + -14x = 0 38 + -19x + -2x2 = 0 + 2x2 + -2x2 38 + -19x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 38 + -19x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -19 + 9.5x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 9.5x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 9.5x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 9.5x + x2 = 0 + 19 9.5x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 9.5x + x2 = 19 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 19 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 19 + 22.5625 Combine like terms: 19 + 22.5625 = 41.5625 22.5625 + 9.5x + x2 = 41.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 41.5625 Calculate the square root of the right side: 6.446898479 Break this problem into two subproblems by setting (x + 4.75) equal to 6.446898479 and -6.446898479.Subproblem 1
x + 4.75 = 6.446898479 Simplifying x + 4.75 = 6.446898479 Reorder the terms: 4.75 + x = 6.446898479 Solving 4.75 + x = 6.446898479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 6.446898479 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 6.446898479 + -4.75 x = 6.446898479 + -4.75 Combine like terms: 6.446898479 + -4.75 = 1.696898479 x = 1.696898479 Simplifying x = 1.696898479Subproblem 2
x + 4.75 = -6.446898479 Simplifying x + 4.75 = -6.446898479 Reorder the terms: 4.75 + x = -6.446898479 Solving 4.75 + x = -6.446898479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -6.446898479 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -6.446898479 + -4.75 x = -6.446898479 + -4.75 Combine like terms: -6.446898479 + -4.75 = -11.196898479 x = -11.196898479 Simplifying x = -11.196898479Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.696898479, -11.196898479}
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