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Simplifying 3x2 + 3x + -246 = 0 Reorder the terms: -246 + 3x + 3x2 = 0 Solving -246 + 3x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-82 + x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-82 + x + x2)' equal to zero and attempt to solve: Simplifying -82 + x + x2 = 0 Solving -82 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + x + 82 + x2 = 0 + 82 Reorder the terms: -82 + 82 + x + x2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + x + x2 = 0 + 82 x + x2 = 0 + 82 Combine like terms: 0 + 82 = 82 x + x2 = 82 The x term is x. 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. x + 0.25 + x2 = 82 + 0.25 Reorder the terms: 0.25 + x + x2 = 82 + 0.25 Combine like terms: 82 + 0.25 = 82.25 0.25 + x + x2 = 82.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + 0.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x + 0.5 = 9.069178574 Simplifying x + 0.5 = 9.069178574 Reorder the terms: 0.5 + x = 9.069178574 Solving 0.5 + x = 9.069178574 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 = 9.069178574 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.069178574 + -0.5 x = 9.069178574 + -0.5 Combine like terms: 9.069178574 + -0.5 = 8.569178574 x = 8.569178574 Simplifying x = 8.569178574Subproblem 2
x + 0.5 = -9.069178574 Simplifying x + 0.5 = -9.069178574 Reorder the terms: 0.5 + x = -9.069178574 Solving 0.5 + x = -9.069178574 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 = -9.069178574 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.069178574 + -0.5 x = -9.069178574 + -0.5 Combine like terms: -9.069178574 + -0.5 = -9.569178574 x = -9.569178574 Simplifying x = -9.569178574Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.569178574, -9.569178574}Solution
x = {8.569178574, -9.569178574}
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