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Simplifying 0 = 6x2 + 3x + -81 Reorder the terms: 0 = -81 + 3x + 6x2 Solving 0 = -81 + 3x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 81 = 81 81 + -3x + -6x2 = -81 + 3x + 6x2 + 81 + -3x + -6x2 Reorder the terms: 81 + -3x + -6x2 = -81 + 81 + 3x + -3x + 6x2 + -6x2 Combine like terms: -81 + 81 = 0 81 + -3x + -6x2 = 0 + 3x + -3x + 6x2 + -6x2 81 + -3x + -6x2 = 3x + -3x + 6x2 + -6x2 Combine like terms: 3x + -3x = 0 81 + -3x + -6x2 = 0 + 6x2 + -6x2 81 + -3x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 81 + -3x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(27 + -1x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(27 + -1x + -2x2)' equal to zero and attempt to solve: Simplifying 27 + -1x + -2x2 = 0 Solving 27 + -1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -13.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 0.5x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 0.5x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 0.5x + x2 = 0 + 13.5 0.5x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 0.5x + x2 = 13.5 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 = 13.5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 13.5 + 0.0625 Combine like terms: 13.5 + 0.0625 = 13.5625 0.0625 + 0.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + 0.25) equal to 3.682729966 and -3.682729966.Subproblem 1
x + 0.25 = 3.682729966 Simplifying x + 0.25 = 3.682729966 Reorder the terms: 0.25 + x = 3.682729966 Solving 0.25 + x = 3.682729966 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 = 3.682729966 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.682729966 + -0.25 x = 3.682729966 + -0.25 Combine like terms: 3.682729966 + -0.25 = 3.432729966 x = 3.432729966 Simplifying x = 3.432729966Subproblem 2
x + 0.25 = -3.682729966 Simplifying x + 0.25 = -3.682729966 Reorder the terms: 0.25 + x = -3.682729966 Solving 0.25 + x = -3.682729966 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 = -3.682729966 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.682729966 + -0.25 x = -3.682729966 + -0.25 Combine like terms: -3.682729966 + -0.25 = -3.932729966 x = -3.932729966 Simplifying x = -3.932729966Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.432729966, -3.932729966}Solution
x = {3.432729966, -3.932729966}
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