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Simplifying 3x2 + -3x + -237 = 0 Reorder the terms: -237 + -3x + 3x2 = 0 Solving -237 + -3x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-79 + -1x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-79 + -1x + x2)' equal to zero and attempt to solve: Simplifying -79 + -1x + x2 = 0 Solving -79 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '79' to each side of the equation. -79 + -1x + 79 + x2 = 0 + 79 Reorder the terms: -79 + 79 + -1x + x2 = 0 + 79 Combine like terms: -79 + 79 = 0 0 + -1x + x2 = 0 + 79 -1x + x2 = 0 + 79 Combine like terms: 0 + 79 = 79 -1x + x2 = 79 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 79 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 79 + 0.25 Combine like terms: 79 + 0.25 = 79.25 0.25 + -1x + x2 = 79.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 79.25 Calculate the square root of the right side: 8.902246907 Break this problem into two subproblems by setting (x + -0.5) equal to 8.902246907 and -8.902246907.Subproblem 1
x + -0.5 = 8.902246907 Simplifying x + -0.5 = 8.902246907 Reorder the terms: -0.5 + x = 8.902246907 Solving -0.5 + x = 8.902246907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 8.902246907 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 8.902246907 + 0.5 x = 8.902246907 + 0.5 Combine like terms: 8.902246907 + 0.5 = 9.402246907 x = 9.402246907 Simplifying x = 9.402246907Subproblem 2
x + -0.5 = -8.902246907 Simplifying x + -0.5 = -8.902246907 Reorder the terms: -0.5 + x = -8.902246907 Solving -0.5 + x = -8.902246907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -8.902246907 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -8.902246907 + 0.5 x = -8.902246907 + 0.5 Combine like terms: -8.902246907 + 0.5 = -8.402246907 x = -8.402246907 Simplifying x = -8.402246907Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.402246907, -8.402246907}Solution
x = {9.402246907, -8.402246907}
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