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Simplifying 3x2 + -33x + -84 = 0 Reorder the terms: -84 + -33x + 3x2 = 0 Solving -84 + -33x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-28 + -11x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-28 + -11x + x2)' equal to zero and attempt to solve: Simplifying -28 + -11x + x2 = 0 Solving -28 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -11x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -11x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -11x + x2 = 0 + 28 -11x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -11x + x2 = 28 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 = 28 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 28 + 30.25 Combine like terms: 28 + 30.25 = 58.25 30.25 + -11x + x2 = 58.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (x + -5.5) equal to 7.632168761 and -7.632168761.Subproblem 1
x + -5.5 = 7.632168761 Simplifying x + -5.5 = 7.632168761 Reorder the terms: -5.5 + x = 7.632168761 Solving -5.5 + x = 7.632168761 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 = 7.632168761 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 7.632168761 + 5.5 x = 7.632168761 + 5.5 Combine like terms: 7.632168761 + 5.5 = 13.132168761 x = 13.132168761 Simplifying x = 13.132168761Subproblem 2
x + -5.5 = -7.632168761 Simplifying x + -5.5 = -7.632168761 Reorder the terms: -5.5 + x = -7.632168761 Solving -5.5 + x = -7.632168761 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 = -7.632168761 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -7.632168761 + 5.5 x = -7.632168761 + 5.5 Combine like terms: -7.632168761 + 5.5 = -2.132168761 x = -2.132168761 Simplifying x = -2.132168761Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.132168761, -2.132168761}Solution
x = {13.132168761, -2.132168761}
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