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Simplifying -33x2 + 12 + -24x = 0 Reorder the terms: 12 + -24x + -33x2 = 0 Solving 12 + -24x + -33x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -8x + -11x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -8x + -11x2)' equal to zero and attempt to solve: Simplifying 4 + -8x + -11x2 = 0 Solving 4 + -8x + -11x2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -0.3636363636 + 0.7272727273x + x2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + 0.7272727273x + 0.3636363636 + x2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + 0.7272727273x + x2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + 0.7272727273x + x2 = 0 + 0.3636363636 0.7272727273x + x2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 0.7272727273x + x2 = 0.3636363636 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 = 0.3636363636 + 0.1322314050 Reorder the terms: 0.1322314050 + 0.7272727273x + x2 = 0.3636363636 + 0.1322314050 Combine like terms: 0.3636363636 + 0.1322314050 = 0.4958677686 0.1322314050 + 0.7272727273x + x2 = 0.4958677686 Factor a perfect square on the left side: (x + 0.3636363637)(x + 0.3636363637) = 0.4958677686 Calculate the square root of the right side: 0.70417879 Break this problem into two subproblems by setting (x + 0.3636363637) equal to 0.70417879 and -0.70417879.Subproblem 1
x + 0.3636363637 = 0.70417879 Simplifying x + 0.3636363637 = 0.70417879 Reorder the terms: 0.3636363637 + x = 0.70417879 Solving 0.3636363637 + x = 0.70417879 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 = 0.70417879 + -0.3636363637 Combine like terms: 0.3636363637 + -0.3636363637 = 0.0000000000 0.0000000000 + x = 0.70417879 + -0.3636363637 x = 0.70417879 + -0.3636363637 Combine like terms: 0.70417879 + -0.3636363637 = 0.3405424263 x = 0.3405424263 Simplifying x = 0.3405424263Subproblem 2
x + 0.3636363637 = -0.70417879 Simplifying x + 0.3636363637 = -0.70417879 Reorder the terms: 0.3636363637 + x = -0.70417879 Solving 0.3636363637 + x = -0.70417879 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 = -0.70417879 + -0.3636363637 Combine like terms: 0.3636363637 + -0.3636363637 = 0.0000000000 0.0000000000 + x = -0.70417879 + -0.3636363637 x = -0.70417879 + -0.3636363637 Combine like terms: -0.70417879 + -0.3636363637 = -1.0678151537 x = -1.0678151537 Simplifying x = -1.0678151537Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3405424263, -1.0678151537}Solution
x = {0.3405424263, -1.0678151537}
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