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Simplifying 6x2 + -3x + -24 = 0 Reorder the terms: -24 + -3x + 6x2 = 0 Solving -24 + -3x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + -1x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -8 + -1x + 2x2 = 0 Solving -8 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + -0.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -0.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.5x + x2 = 0 + 4 -0.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.5x + x2 = 4 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 4 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 4 + 0.0625 Combine like terms: 4 + 0.0625 = 4.0625 0.0625 + -0.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + -0.25) equal to 2.015564437 and -2.015564437.Subproblem 1
x + -0.25 = 2.015564437 Simplifying x + -0.25 = 2.015564437 Reorder the terms: -0.25 + x = 2.015564437 Solving -0.25 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.015564437 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.015564437 + 0.25 x = 2.015564437 + 0.25 Combine like terms: 2.015564437 + 0.25 = 2.265564437 x = 2.265564437 Simplifying x = 2.265564437Subproblem 2
x + -0.25 = -2.015564437 Simplifying x + -0.25 = -2.015564437 Reorder the terms: -0.25 + x = -2.015564437 Solving -0.25 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.015564437 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.015564437 + 0.25 x = -2.015564437 + 0.25 Combine like terms: -2.015564437 + 0.25 = -1.765564437 x = -1.765564437 Simplifying x = -1.765564437Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.265564437, -1.765564437}Solution
x = {2.265564437, -1.765564437}
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