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Simplifying (5x + -22)(4x + 4) = 90 Reorder the terms: (-22 + 5x)(4x + 4) = 90 Reorder the terms: (-22 + 5x)(4 + 4x) = 90 Multiply (-22 + 5x) * (4 + 4x) (-22(4 + 4x) + 5x * (4 + 4x)) = 90 ((4 * -22 + 4x * -22) + 5x * (4 + 4x)) = 90 ((-88 + -88x) + 5x * (4 + 4x)) = 90 (-88 + -88x + (4 * 5x + 4x * 5x)) = 90 (-88 + -88x + (20x + 20x2)) = 90 Combine like terms: -88x + 20x = -68x (-88 + -68x + 20x2) = 90 Solving -88 + -68x + 20x2 = 90 Solving for variable 'x'. Reorder the terms: -88 + -90 + -68x + 20x2 = 90 + -90 Combine like terms: -88 + -90 = -178 -178 + -68x + 20x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -178 + -68x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-89 + -34x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-89 + -34x + 10x2)' equal to zero and attempt to solve: Simplifying -89 + -34x + 10x2 = 0 Solving -89 + -34x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -8.9 + -3.4x + x2 = 0.0 Move the constant term to the right: Add '8.9' to each side of the equation. -8.9 + -3.4x + 8.9 + x2 = 0.0 + 8.9 Reorder the terms: -8.9 + 8.9 + -3.4x + x2 = 0.0 + 8.9 Combine like terms: -8.9 + 8.9 = 0.0 0.0 + -3.4x + x2 = 0.0 + 8.9 -3.4x + x2 = 0.0 + 8.9 Combine like terms: 0.0 + 8.9 = 8.9 -3.4x + x2 = 8.9 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 = 8.9 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 8.9 + 2.89 Combine like terms: 8.9 + 2.89 = 11.79 2.89 + -3.4x + x2 = 11.79 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 11.79 Calculate the square root of the right side: 3.433656943 Break this problem into two subproblems by setting (x + -1.7) equal to 3.433656943 and -3.433656943.Subproblem 1
x + -1.7 = 3.433656943 Simplifying x + -1.7 = 3.433656943 Reorder the terms: -1.7 + x = 3.433656943 Solving -1.7 + x = 3.433656943 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 = 3.433656943 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 3.433656943 + 1.7 x = 3.433656943 + 1.7 Combine like terms: 3.433656943 + 1.7 = 5.133656943 x = 5.133656943 Simplifying x = 5.133656943Subproblem 2
x + -1.7 = -3.433656943 Simplifying x + -1.7 = -3.433656943 Reorder the terms: -1.7 + x = -3.433656943 Solving -1.7 + x = -3.433656943 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 = -3.433656943 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -3.433656943 + 1.7 x = -3.433656943 + 1.7 Combine like terms: -3.433656943 + 1.7 = -1.733656943 x = -1.733656943 Simplifying x = -1.733656943Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.133656943, -1.733656943}Solution
x = {5.133656943, -1.733656943}
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