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Simplifying (4x + 5)(2x + 17) = 180 Reorder the terms: (5 + 4x)(2x + 17) = 180 Reorder the terms: (5 + 4x)(17 + 2x) = 180 Multiply (5 + 4x) * (17 + 2x) (5(17 + 2x) + 4x * (17 + 2x)) = 180 ((17 * 5 + 2x * 5) + 4x * (17 + 2x)) = 180 ((85 + 10x) + 4x * (17 + 2x)) = 180 (85 + 10x + (17 * 4x + 2x * 4x)) = 180 (85 + 10x + (68x + 8x2)) = 180 Combine like terms: 10x + 68x = 78x (85 + 78x + 8x2) = 180 Solving 85 + 78x + 8x2 = 180 Solving for variable 'x'. Reorder the terms: 85 + -180 + 78x + 8x2 = 180 + -180 Combine like terms: 85 + -180 = -95 -95 + 78x + 8x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -95 + 78x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -11.875 + 9.75x + x2 = 0 Move the constant term to the right: Add '11.875' to each side of the equation. -11.875 + 9.75x + 11.875 + x2 = 0 + 11.875 Reorder the terms: -11.875 + 11.875 + 9.75x + x2 = 0 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + 9.75x + x2 = 0 + 11.875 9.75x + x2 = 0 + 11.875 Combine like terms: 0 + 11.875 = 11.875 9.75x + x2 = 11.875 The x term is 9.75x. Take half its coefficient (4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. 9.75x + 23.765625 + x2 = 11.875 + 23.765625 Reorder the terms: 23.765625 + 9.75x + x2 = 11.875 + 23.765625 Combine like terms: 11.875 + 23.765625 = 35.640625 23.765625 + 9.75x + x2 = 35.640625 Factor a perfect square on the left side: (x + 4.875)(x + 4.875) = 35.640625 Calculate the square root of the right side: 5.969976968 Break this problem into two subproblems by setting (x + 4.875) equal to 5.969976968 and -5.969976968.Subproblem 1
x + 4.875 = 5.969976968 Simplifying x + 4.875 = 5.969976968 Reorder the terms: 4.875 + x = 5.969976968 Solving 4.875 + x = 5.969976968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.875' to each side of the equation. 4.875 + -4.875 + x = 5.969976968 + -4.875 Combine like terms: 4.875 + -4.875 = 0.000 0.000 + x = 5.969976968 + -4.875 x = 5.969976968 + -4.875 Combine like terms: 5.969976968 + -4.875 = 1.094976968 x = 1.094976968 Simplifying x = 1.094976968Subproblem 2
x + 4.875 = -5.969976968 Simplifying x + 4.875 = -5.969976968 Reorder the terms: 4.875 + x = -5.969976968 Solving 4.875 + x = -5.969976968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.875' to each side of the equation. 4.875 + -4.875 + x = -5.969976968 + -4.875 Combine like terms: 4.875 + -4.875 = 0.000 0.000 + x = -5.969976968 + -4.875 x = -5.969976968 + -4.875 Combine like terms: -5.969976968 + -4.875 = -10.844976968 x = -10.844976968 Simplifying x = -10.844976968Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.094976968, -10.844976968}
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