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Simplifying (5x + -22)(4x + 4) = 180 Reorder the terms: (-22 + 5x)(4x + 4) = 180 Reorder the terms: (-22 + 5x)(4 + 4x) = 180 Multiply (-22 + 5x) * (4 + 4x) (-22(4 + 4x) + 5x * (4 + 4x)) = 180 ((4 * -22 + 4x * -22) + 5x * (4 + 4x)) = 180 ((-88 + -88x) + 5x * (4 + 4x)) = 180 (-88 + -88x + (4 * 5x + 4x * 5x)) = 180 (-88 + -88x + (20x + 20x2)) = 180 Combine like terms: -88x + 20x = -68x (-88 + -68x + 20x2) = 180 Solving -88 + -68x + 20x2 = 180 Solving for variable 'x'. Reorder the terms: -88 + -180 + -68x + 20x2 = 180 + -180 Combine like terms: -88 + -180 = -268 -268 + -68x + 20x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -268 + -68x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-67 + -17x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-67 + -17x + 5x2)' equal to zero and attempt to solve: Simplifying -67 + -17x + 5x2 = 0 Solving -67 + -17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -13.4 + -3.4x + x2 = 0 Move the constant term to the right: Add '13.4' to each side of the equation. -13.4 + -3.4x + 13.4 + x2 = 0 + 13.4 Reorder the terms: -13.4 + 13.4 + -3.4x + x2 = 0 + 13.4 Combine like terms: -13.4 + 13.4 = 0.0 0.0 + -3.4x + x2 = 0 + 13.4 -3.4x + x2 = 0 + 13.4 Combine like terms: 0 + 13.4 = 13.4 -3.4x + x2 = 13.4 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 = 13.4 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 13.4 + 2.89 Combine like terms: 13.4 + 2.89 = 16.29 2.89 + -3.4x + x2 = 16.29 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 16.29 Calculate the square root of the right side: 4.036087214 Break this problem into two subproblems by setting (x + -1.7) equal to 4.036087214 and -4.036087214.Subproblem 1
x + -1.7 = 4.036087214 Simplifying x + -1.7 = 4.036087214 Reorder the terms: -1.7 + x = 4.036087214 Solving -1.7 + x = 4.036087214 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 = 4.036087214 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 4.036087214 + 1.7 x = 4.036087214 + 1.7 Combine like terms: 4.036087214 + 1.7 = 5.736087214 x = 5.736087214 Simplifying x = 5.736087214Subproblem 2
x + -1.7 = -4.036087214 Simplifying x + -1.7 = -4.036087214 Reorder the terms: -1.7 + x = -4.036087214 Solving -1.7 + x = -4.036087214 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 = -4.036087214 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -4.036087214 + 1.7 x = -4.036087214 + 1.7 Combine like terms: -4.036087214 + 1.7 = -2.336087214 x = -2.336087214 Simplifying x = -2.336087214Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.736087214, -2.336087214}Solution
x = {5.736087214, -2.336087214}
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