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Simplifying (x + -4)(2x + -3) = 5 Reorder the terms: (-4 + x)(2x + -3) = 5 Reorder the terms: (-4 + x)(-3 + 2x) = 5 Multiply (-4 + x) * (-3 + 2x) (-4(-3 + 2x) + x(-3 + 2x)) = 5 ((-3 * -4 + 2x * -4) + x(-3 + 2x)) = 5 ((12 + -8x) + x(-3 + 2x)) = 5 (12 + -8x + (-3 * x + 2x * x)) = 5 (12 + -8x + (-3x + 2x2)) = 5 Combine like terms: -8x + -3x = -11x (12 + -11x + 2x2) = 5 Solving 12 + -11x + 2x2 = 5 Solving for variable 'x'. Reorder the terms: 12 + -5 + -11x + 2x2 = 5 + -5 Combine like terms: 12 + -5 = 7 7 + -11x + 2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 7 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -5.5x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -5.5x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -5.5x + x2 = 0 + -3.5 -5.5x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -5.5x + x2 = -3.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -3.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -3.5 + 7.5625 Combine like terms: -3.5 + 7.5625 = 4.0625 7.5625 + -5.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + -2.75) equal to 2.015564437 and -2.015564437.Subproblem 1
x + -2.75 = 2.015564437 Simplifying x + -2.75 = 2.015564437 Reorder the terms: -2.75 + x = 2.015564437 Solving -2.75 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.015564437 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.015564437 + 2.75 x = 2.015564437 + 2.75 Combine like terms: 2.015564437 + 2.75 = 4.765564437 x = 4.765564437 Simplifying x = 4.765564437Subproblem 2
x + -2.75 = -2.015564437 Simplifying x + -2.75 = -2.015564437 Reorder the terms: -2.75 + x = -2.015564437 Solving -2.75 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.015564437 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.015564437 + 2.75 x = -2.015564437 + 2.75 Combine like terms: -2.015564437 + 2.75 = 0.734435563 x = 0.734435563 Simplifying x = 0.734435563Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.765564437, 0.734435563}
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