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Simplifying 6x2 + -24x + -33 = 0 Reorder the terms: -33 + -24x + 6x2 = 0 Solving -33 + -24x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-11 + -8x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + -8x + 2x2)' equal to zero and attempt to solve: Simplifying -11 + -8x + 2x2 = 0 Solving -11 + -8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + -4x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -4x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -4x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -4x + x2 = 0 + 5.5 -4x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -4x + x2 = 5.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 5.5 + 4 Reorder the terms: 4 + -4x + x2 = 5.5 + 4 Combine like terms: 5.5 + 4 = 9.5 4 + -4x + x2 = 9.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (x + -2) equal to 3.082207001 and -3.082207001.Subproblem 1
x + -2 = 3.082207001 Simplifying x + -2 = 3.082207001 Reorder the terms: -2 + x = 3.082207001 Solving -2 + x = 3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.082207001 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.082207001 + 2 x = 3.082207001 + 2 Combine like terms: 3.082207001 + 2 = 5.082207001 x = 5.082207001 Simplifying x = 5.082207001Subproblem 2
x + -2 = -3.082207001 Simplifying x + -2 = -3.082207001 Reorder the terms: -2 + x = -3.082207001 Solving -2 + x = -3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.082207001 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.082207001 + 2 x = -3.082207001 + 2 Combine like terms: -3.082207001 + 2 = -1.082207001 x = -1.082207001 Simplifying x = -1.082207001Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.082207001, -1.082207001}Solution
x = {5.082207001, -1.082207001}
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