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Simplifying 452x + -27 = 3x2 Reorder the terms: -27 + 452x = 3x2 Solving -27 + 452x = 3x2 Solving for variable 'x'. Combine like terms: 3x2 + -3x2 = 0 -27 + 452x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 9 + -150.6666667x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -150.6666667x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -150.6666667x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -150.6666667x + x2 = 0 + -9 -150.6666667x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -150.6666667x + x2 = -9 The x term is -150.6666667x. Take half its coefficient (-75.33333335). Square it (5675.111114) and add it to both sides. Add '5675.111114' to each side of the equation. -150.6666667x + 5675.111114 + x2 = -9 + 5675.111114 Reorder the terms: 5675.111114 + -150.6666667x + x2 = -9 + 5675.111114 Combine like terms: -9 + 5675.111114 = 5666.111114 5675.111114 + -150.6666667x + x2 = 5666.111114 Factor a perfect square on the left side: (x + -75.33333335)(x + -75.33333335) = 5666.111114 Calculate the square root of the right side: 75.273575138 Break this problem into two subproblems by setting (x + -75.33333335) equal to 75.273575138 and -75.273575138.Subproblem 1
x + -75.33333335 = 75.273575138 Simplifying x + -75.33333335 = 75.273575138 Reorder the terms: -75.33333335 + x = 75.273575138 Solving -75.33333335 + x = 75.273575138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75.33333335' to each side of the equation. -75.33333335 + 75.33333335 + x = 75.273575138 + 75.33333335 Combine like terms: -75.33333335 + 75.33333335 = 0.00000000 0.00000000 + x = 75.273575138 + 75.33333335 x = 75.273575138 + 75.33333335 Combine like terms: 75.273575138 + 75.33333335 = 150.606908488 x = 150.606908488 Simplifying x = 150.606908488Subproblem 2
x + -75.33333335 = -75.273575138 Simplifying x + -75.33333335 = -75.273575138 Reorder the terms: -75.33333335 + x = -75.273575138 Solving -75.33333335 + x = -75.273575138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75.33333335' to each side of the equation. -75.33333335 + 75.33333335 + x = -75.273575138 + 75.33333335 Combine like terms: -75.33333335 + 75.33333335 = 0.00000000 0.00000000 + x = -75.273575138 + 75.33333335 x = -75.273575138 + 75.33333335 Combine like terms: -75.273575138 + 75.33333335 = 0.059758212 x = 0.059758212 Simplifying x = 0.059758212Solution
The solution to the problem is based on the solutions from the subproblems. x = {150.606908488, 0.059758212}
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