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Simplifying (9x + -14)(x + 74) = 180 Reorder the terms: (-14 + 9x)(x + 74) = 180 Reorder the terms: (-14 + 9x)(74 + x) = 180 Multiply (-14 + 9x) * (74 + x) (-14(74 + x) + 9x * (74 + x)) = 180 ((74 * -14 + x * -14) + 9x * (74 + x)) = 180 ((-1036 + -14x) + 9x * (74 + x)) = 180 (-1036 + -14x + (74 * 9x + x * 9x)) = 180 (-1036 + -14x + (666x + 9x2)) = 180 Combine like terms: -14x + 666x = 652x (-1036 + 652x + 9x2) = 180 Solving -1036 + 652x + 9x2 = 180 Solving for variable 'x'. Reorder the terms: -1036 + -180 + 652x + 9x2 = 180 + -180 Combine like terms: -1036 + -180 = -1216 -1216 + 652x + 9x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -1216 + 652x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -135.1111111 + 72.44444444x + x2 = 0 Move the constant term to the right: Add '135.1111111' to each side of the equation. -135.1111111 + 72.44444444x + 135.1111111 + x2 = 0 + 135.1111111 Reorder the terms: -135.1111111 + 135.1111111 + 72.44444444x + x2 = 0 + 135.1111111 Combine like terms: -135.1111111 + 135.1111111 = 0.0000000 0.0000000 + 72.44444444x + x2 = 0 + 135.1111111 72.44444444x + x2 = 0 + 135.1111111 Combine like terms: 0 + 135.1111111 = 135.1111111 72.44444444x + x2 = 135.1111111 The x term is 72.44444444x. Take half its coefficient (36.22222222). Square it (1312.049383) and add it to both sides. Add '1312.049383' to each side of the equation. 72.44444444x + 1312.049383 + x2 = 135.1111111 + 1312.049383 Reorder the terms: 1312.049383 + 72.44444444x + x2 = 135.1111111 + 1312.049383 Combine like terms: 135.1111111 + 1312.049383 = 1447.1604941 1312.049383 + 72.44444444x + x2 = 1447.1604941 Factor a perfect square on the left side: (x + 36.22222222)(x + 36.22222222) = 1447.1604941 Calculate the square root of the right side: 38.041562719 Break this problem into two subproblems by setting (x + 36.22222222) equal to 38.041562719 and -38.041562719.Subproblem 1
x + 36.22222222 = 38.041562719 Simplifying x + 36.22222222 = 38.041562719 Reorder the terms: 36.22222222 + x = 38.041562719 Solving 36.22222222 + x = 38.041562719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36.22222222' to each side of the equation. 36.22222222 + -36.22222222 + x = 38.041562719 + -36.22222222 Combine like terms: 36.22222222 + -36.22222222 = 0.00000000 0.00000000 + x = 38.041562719 + -36.22222222 x = 38.041562719 + -36.22222222 Combine like terms: 38.041562719 + -36.22222222 = 1.819340499 x = 1.819340499 Simplifying x = 1.819340499Subproblem 2
x + 36.22222222 = -38.041562719 Simplifying x + 36.22222222 = -38.041562719 Reorder the terms: 36.22222222 + x = -38.041562719 Solving 36.22222222 + x = -38.041562719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36.22222222' to each side of the equation. 36.22222222 + -36.22222222 + x = -38.041562719 + -36.22222222 Combine like terms: 36.22222222 + -36.22222222 = 0.00000000 0.00000000 + x = -38.041562719 + -36.22222222 x = -38.041562719 + -36.22222222 Combine like terms: -38.041562719 + -36.22222222 = -74.263784939 x = -74.263784939 Simplifying x = -74.263784939Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.819340499, -74.263784939}
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