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Simplifying 45 = (0.333x + 2)(x) Reorder the terms: 45 = (2 + 0.333x)(x) Reorder the terms for easier multiplication: 45 = x(2 + 0.333x) 45 = (2 * x + 0.333x * x) 45 = (2x + 0.333x2) Solving 45 = 2x + 0.333x2 Solving for variable 'x'. Reorder the terms: 45 + -2x + -0.333x2 = 2x + -2x + 0.333x2 + -0.333x2 Combine like terms: 2x + -2x = 0 45 + -2x + -0.333x2 = 0 + 0.333x2 + -0.333x2 45 + -2x + -0.333x2 = 0.333x2 + -0.333x2 Combine like terms: 0.333x2 + -0.333x2 = 0.000 45 + -2x + -0.333x2 = 0.000 Begin completing the square. Divide all terms by -0.333 the coefficient of the squared term: Divide each side by '-0.333'. -135.1351351 + 6.006006006x + x2 = 0 Move the constant term to the right: Add '135.1351351' to each side of the equation. -135.1351351 + 6.006006006x + 135.1351351 + x2 = 0 + 135.1351351 Reorder the terms: -135.1351351 + 135.1351351 + 6.006006006x + x2 = 0 + 135.1351351 Combine like terms: -135.1351351 + 135.1351351 = 0.0000000 0.0000000 + 6.006006006x + x2 = 0 + 135.1351351 6.006006006x + x2 = 0 + 135.1351351 Combine like terms: 0 + 135.1351351 = 135.1351351 6.006006006x + x2 = 135.1351351 The x term is 6.006006006x. Take half its coefficient (3.003003003). Square it (9.018027036) and add it to both sides. Add '9.018027036' to each side of the equation. 6.006006006x + 9.018027036 + x2 = 135.1351351 + 9.018027036 Reorder the terms: 9.018027036 + 6.006006006x + x2 = 135.1351351 + 9.018027036 Combine like terms: 135.1351351 + 9.018027036 = 144.153162136 9.018027036 + 6.006006006x + x2 = 144.153162136 Factor a perfect square on the left side: (x + 3.003003003)(x + 3.003003003) = 144.153162136 Calculate the square root of the right side: 12.00638006 Break this problem into two subproblems by setting (x + 3.003003003) equal to 12.00638006 and -12.00638006.Subproblem 1
x + 3.003003003 = 12.00638006 Simplifying x + 3.003003003 = 12.00638006 Reorder the terms: 3.003003003 + x = 12.00638006 Solving 3.003003003 + x = 12.00638006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.003003003' to each side of the equation. 3.003003003 + -3.003003003 + x = 12.00638006 + -3.003003003 Combine like terms: 3.003003003 + -3.003003003 = 0.000000000 0.000000000 + x = 12.00638006 + -3.003003003 x = 12.00638006 + -3.003003003 Combine like terms: 12.00638006 + -3.003003003 = 9.003377057 x = 9.003377057 Simplifying x = 9.003377057Subproblem 2
x + 3.003003003 = -12.00638006 Simplifying x + 3.003003003 = -12.00638006 Reorder the terms: 3.003003003 + x = -12.00638006 Solving 3.003003003 + x = -12.00638006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.003003003' to each side of the equation. 3.003003003 + -3.003003003 + x = -12.00638006 + -3.003003003 Combine like terms: 3.003003003 + -3.003003003 = 0.000000000 0.000000000 + x = -12.00638006 + -3.003003003 x = -12.00638006 + -3.003003003 Combine like terms: -12.00638006 + -3.003003003 = -15.009383063 x = -15.009383063 Simplifying x = -15.009383063Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.003377057, -15.009383063}
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