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Simplifying -3x2 + 4323 + -33x = 0 Reorder the terms: 4323 + -33x + -3x2 = 0 Solving 4323 + -33x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1441 + -11x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1441 + -11x + -1x2)' equal to zero and attempt to solve: Simplifying 1441 + -11x + -1x2 = 0 Solving 1441 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1441 + 11x + x2 = 0 Move the constant term to the right: Add '1441' to each side of the equation. -1441 + 11x + 1441 + x2 = 0 + 1441 Reorder the terms: -1441 + 1441 + 11x + x2 = 0 + 1441 Combine like terms: -1441 + 1441 = 0 0 + 11x + x2 = 0 + 1441 11x + x2 = 0 + 1441 Combine like terms: 0 + 1441 = 1441 11x + x2 = 1441 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 1441 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 1441 + 30.25 Combine like terms: 1441 + 30.25 = 1471.25 30.25 + 11x + x2 = 1471.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 1471.25 Calculate the square root of the right side: 38.356876828 Break this problem into two subproblems by setting (x + 5.5) equal to 38.356876828 and -38.356876828.Subproblem 1
x + 5.5 = 38.356876828 Simplifying x + 5.5 = 38.356876828 Reorder the terms: 5.5 + x = 38.356876828 Solving 5.5 + x = 38.356876828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 38.356876828 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 38.356876828 + -5.5 x = 38.356876828 + -5.5 Combine like terms: 38.356876828 + -5.5 = 32.856876828 x = 32.856876828 Simplifying x = 32.856876828Subproblem 2
x + 5.5 = -38.356876828 Simplifying x + 5.5 = -38.356876828 Reorder the terms: 5.5 + x = -38.356876828 Solving 5.5 + x = -38.356876828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -38.356876828 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -38.356876828 + -5.5 x = -38.356876828 + -5.5 Combine like terms: -38.356876828 + -5.5 = -43.856876828 x = -43.856876828 Simplifying x = -43.856876828Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.856876828, -43.856876828}Solution
x = {32.856876828, -43.856876828}
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