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Simplifying 0 = x2 + -33x + 232 Reorder the terms: 0 = 232 + -33x + x2 Solving 0 = 232 + -33x + x2 Solving for variable 'x'. Combine like terms: 0 + -232 = -232 -232 + 33x + -1x2 = 232 + -33x + x2 + -232 + 33x + -1x2 Reorder the terms: -232 + 33x + -1x2 = 232 + -232 + -33x + 33x + x2 + -1x2 Combine like terms: 232 + -232 = 0 -232 + 33x + -1x2 = 0 + -33x + 33x + x2 + -1x2 -232 + 33x + -1x2 = -33x + 33x + x2 + -1x2 Combine like terms: -33x + 33x = 0 -232 + 33x + -1x2 = 0 + x2 + -1x2 -232 + 33x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -232 + 33x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 232 + -33x + x2 = 0 Move the constant term to the right: Add '-232' to each side of the equation. 232 + -33x + -232 + x2 = 0 + -232 Reorder the terms: 232 + -232 + -33x + x2 = 0 + -232 Combine like terms: 232 + -232 = 0 0 + -33x + x2 = 0 + -232 -33x + x2 = 0 + -232 Combine like terms: 0 + -232 = -232 -33x + x2 = -232 The x term is -33x. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33x + 272.25 + x2 = -232 + 272.25 Reorder the terms: 272.25 + -33x + x2 = -232 + 272.25 Combine like terms: -232 + 272.25 = 40.25 272.25 + -33x + x2 = 40.25 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + -16.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + -16.5 = 6.34428877 Simplifying x + -16.5 = 6.34428877 Reorder the terms: -16.5 + x = 6.34428877 Solving -16.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = 6.34428877 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 6.34428877 + 16.5 x = 6.34428877 + 16.5 Combine like terms: 6.34428877 + 16.5 = 22.84428877 x = 22.84428877 Simplifying x = 22.84428877Subproblem 2
x + -16.5 = -6.34428877 Simplifying x + -16.5 = -6.34428877 Reorder the terms: -16.5 + x = -6.34428877 Solving -16.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = -6.34428877 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -6.34428877 + 16.5 x = -6.34428877 + 16.5 Combine like terms: -6.34428877 + 16.5 = 10.15571123 x = 10.15571123 Simplifying x = 10.15571123Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.84428877, 10.15571123}
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