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Simplifying 33x2 + -24x + -30 = 0 Reorder the terms: -30 + -24x + 33x2 = 0 Solving -30 + -24x + 33x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + -8x + 11x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + -8x + 11x2)' equal to zero and attempt to solve: Simplifying -10 + -8x + 11x2 = 0 Solving -10 + -8x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.9090909091 + -0.7272727273x + x2 = 0 Move the constant term to the right: Add '0.9090909091' to each side of the equation. -0.9090909091 + -0.7272727273x + 0.9090909091 + x2 = 0 + 0.9090909091 Reorder the terms: -0.9090909091 + 0.9090909091 + -0.7272727273x + x2 = 0 + 0.9090909091 Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000 0.0000000000 + -0.7272727273x + x2 = 0 + 0.9090909091 -0.7272727273x + x2 = 0 + 0.9090909091 Combine like terms: 0 + 0.9090909091 = 0.9090909091 -0.7272727273x + x2 = 0.9090909091 The x term is -0.7272727273x. Take half its coefficient (-0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. -0.7272727273x + 0.1322314050 + x2 = 0.9090909091 + 0.1322314050 Reorder the terms: 0.1322314050 + -0.7272727273x + x2 = 0.9090909091 + 0.1322314050 Combine like terms: 0.9090909091 + 0.1322314050 = 1.0413223141 0.1322314050 + -0.7272727273x + x2 = 1.0413223141 Factor a perfect square on the left side: (x + -0.3636363637)(x + -0.3636363637) = 1.0413223141 Calculate the square root of the right side: 1.020452015 Break this problem into two subproblems by setting (x + -0.3636363637) equal to 1.020452015 and -1.020452015.Subproblem 1
x + -0.3636363637 = 1.020452015 Simplifying x + -0.3636363637 = 1.020452015 Reorder the terms: -0.3636363637 + x = 1.020452015 Solving -0.3636363637 + x = 1.020452015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = 1.020452015 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = 1.020452015 + 0.3636363637 x = 1.020452015 + 0.3636363637 Combine like terms: 1.020452015 + 0.3636363637 = 1.3840883787 x = 1.3840883787 Simplifying x = 1.3840883787Subproblem 2
x + -0.3636363637 = -1.020452015 Simplifying x + -0.3636363637 = -1.020452015 Reorder the terms: -0.3636363637 + x = -1.020452015 Solving -0.3636363637 + x = -1.020452015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = -1.020452015 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = -1.020452015 + 0.3636363637 x = -1.020452015 + 0.3636363637 Combine like terms: -1.020452015 + 0.3636363637 = -0.6568156513 x = -0.6568156513 Simplifying x = -0.6568156513Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3840883787, -0.6568156513}Solution
x = {1.3840883787, -0.6568156513}
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