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Simplifying 6x2 + -3x + -96 = 0 Reorder the terms: -96 + -3x + 6x2 = 0 Solving -96 + -3x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-32 + -1x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-32 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -32 + -1x + 2x2 = 0 Solving -32 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16 + -0.5x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -0.5x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -0.5x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -0.5x + x2 = 0 + 16 -0.5x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -0.5x + x2 = 16 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 = 16 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 16 + 0.0625 Combine like terms: 16 + 0.0625 = 16.0625 0.0625 + -0.5x + x2 = 16.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 16.0625 Calculate the square root of the right side: 4.007804885 Break this problem into two subproblems by setting (x + -0.25) equal to 4.007804885 and -4.007804885.Subproblem 1
x + -0.25 = 4.007804885 Simplifying x + -0.25 = 4.007804885 Reorder the terms: -0.25 + x = 4.007804885 Solving -0.25 + x = 4.007804885 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 = 4.007804885 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 4.007804885 + 0.25 x = 4.007804885 + 0.25 Combine like terms: 4.007804885 + 0.25 = 4.257804885 x = 4.257804885 Simplifying x = 4.257804885Subproblem 2
x + -0.25 = -4.007804885 Simplifying x + -0.25 = -4.007804885 Reorder the terms: -0.25 + x = -4.007804885 Solving -0.25 + x = -4.007804885 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 = -4.007804885 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -4.007804885 + 0.25 x = -4.007804885 + 0.25 Combine like terms: -4.007804885 + 0.25 = -3.757804885 x = -3.757804885 Simplifying x = -3.757804885Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.257804885, -3.757804885}Solution
x = {4.257804885, -3.757804885}
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