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Simplifying (4x + 4)(5x + -22) = 45 Reorder the terms: (4 + 4x)(5x + -22) = 45 Reorder the terms: (4 + 4x)(-22 + 5x) = 45 Multiply (4 + 4x) * (-22 + 5x) (4(-22 + 5x) + 4x * (-22 + 5x)) = 45 ((-22 * 4 + 5x * 4) + 4x * (-22 + 5x)) = 45 ((-88 + 20x) + 4x * (-22 + 5x)) = 45 (-88 + 20x + (-22 * 4x + 5x * 4x)) = 45 (-88 + 20x + (-88x + 20x2)) = 45 Combine like terms: 20x + -88x = -68x (-88 + -68x + 20x2) = 45 Solving -88 + -68x + 20x2 = 45 Solving for variable 'x'. Reorder the terms: -88 + -45 + -68x + 20x2 = 45 + -45 Combine like terms: -88 + -45 = -133 -133 + -68x + 20x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -133 + -68x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -6.65 + -3.4x + x2 = 0.0 Move the constant term to the right: Add '6.65' to each side of the equation. -6.65 + -3.4x + 6.65 + x2 = 0.0 + 6.65 Reorder the terms: -6.65 + 6.65 + -3.4x + x2 = 0.0 + 6.65 Combine like terms: -6.65 + 6.65 = 0.00 0.00 + -3.4x + x2 = 0.0 + 6.65 -3.4x + x2 = 0.0 + 6.65 Combine like terms: 0.0 + 6.65 = 6.65 -3.4x + x2 = 6.65 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = 6.65 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 6.65 + 2.89 Combine like terms: 6.65 + 2.89 = 9.54 2.89 + -3.4x + x2 = 9.54 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 9.54 Calculate the square root of the right side: 3.088689042 Break this problem into two subproblems by setting (x + -1.7) equal to 3.088689042 and -3.088689042.Subproblem 1
x + -1.7 = 3.088689042 Simplifying x + -1.7 = 3.088689042 Reorder the terms: -1.7 + x = 3.088689042 Solving -1.7 + x = 3.088689042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 3.088689042 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 3.088689042 + 1.7 x = 3.088689042 + 1.7 Combine like terms: 3.088689042 + 1.7 = 4.788689042 x = 4.788689042 Simplifying x = 4.788689042Subproblem 2
x + -1.7 = -3.088689042 Simplifying x + -1.7 = -3.088689042 Reorder the terms: -1.7 + x = -3.088689042 Solving -1.7 + x = -3.088689042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -3.088689042 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -3.088689042 + 1.7 x = -3.088689042 + 1.7 Combine like terms: -3.088689042 + 1.7 = -1.388689042 x = -1.388689042 Simplifying x = -1.388689042Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.788689042, -1.388689042}
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