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Simplifying (5x + -22)(4x + 4) = 990 Reorder the terms: (-22 + 5x)(4x + 4) = 990 Reorder the terms: (-22 + 5x)(4 + 4x) = 990 Multiply (-22 + 5x) * (4 + 4x) (-22(4 + 4x) + 5x * (4 + 4x)) = 990 ((4 * -22 + 4x * -22) + 5x * (4 + 4x)) = 990 ((-88 + -88x) + 5x * (4 + 4x)) = 990 (-88 + -88x + (4 * 5x + 4x * 5x)) = 990 (-88 + -88x + (20x + 20x2)) = 990 Combine like terms: -88x + 20x = -68x (-88 + -68x + 20x2) = 990 Solving -88 + -68x + 20x2 = 990 Solving for variable 'x'. Reorder the terms: -88 + -990 + -68x + 20x2 = 990 + -990 Combine like terms: -88 + -990 = -1078 -1078 + -68x + 20x2 = 990 + -990 Combine like terms: 990 + -990 = 0 -1078 + -68x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-539 + -34x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-539 + -34x + 10x2)' equal to zero and attempt to solve: Simplifying -539 + -34x + 10x2 = 0 Solving -539 + -34x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -53.9 + -3.4x + x2 = 0.0 Move the constant term to the right: Add '53.9' to each side of the equation. -53.9 + -3.4x + 53.9 + x2 = 0.0 + 53.9 Reorder the terms: -53.9 + 53.9 + -3.4x + x2 = 0.0 + 53.9 Combine like terms: -53.9 + 53.9 = 0.0 0.0 + -3.4x + x2 = 0.0 + 53.9 -3.4x + x2 = 0.0 + 53.9 Combine like terms: 0.0 + 53.9 = 53.9 -3.4x + x2 = 53.9 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 = 53.9 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 53.9 + 2.89 Combine like terms: 53.9 + 2.89 = 56.79 2.89 + -3.4x + x2 = 56.79 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 56.79 Calculate the square root of the right side: 7.535914012 Break this problem into two subproblems by setting (x + -1.7) equal to 7.535914012 and -7.535914012.Subproblem 1
x + -1.7 = 7.535914012 Simplifying x + -1.7 = 7.535914012 Reorder the terms: -1.7 + x = 7.535914012 Solving -1.7 + x = 7.535914012 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 = 7.535914012 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 7.535914012 + 1.7 x = 7.535914012 + 1.7 Combine like terms: 7.535914012 + 1.7 = 9.235914012 x = 9.235914012 Simplifying x = 9.235914012Subproblem 2
x + -1.7 = -7.535914012 Simplifying x + -1.7 = -7.535914012 Reorder the terms: -1.7 + x = -7.535914012 Solving -1.7 + x = -7.535914012 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 = -7.535914012 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -7.535914012 + 1.7 x = -7.535914012 + 1.7 Combine like terms: -7.535914012 + 1.7 = -5.835914012 x = -5.835914012 Simplifying x = -5.835914012Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.235914012, -5.835914012}Solution
x = {9.235914012, -5.835914012}
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