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Simplifying 6x2 + -3x + -86 = 0 Reorder the terms: -86 + -3x + 6x2 = 0 Solving -86 + -3x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -14.33333333 + -0.5x + x2 = 0 Move the constant term to the right: Add '14.33333333' to each side of the equation. -14.33333333 + -0.5x + 14.33333333 + x2 = 0 + 14.33333333 Reorder the terms: -14.33333333 + 14.33333333 + -0.5x + x2 = 0 + 14.33333333 Combine like terms: -14.33333333 + 14.33333333 = 0.00000000 0.00000000 + -0.5x + x2 = 0 + 14.33333333 -0.5x + x2 = 0 + 14.33333333 Combine like terms: 0 + 14.33333333 = 14.33333333 -0.5x + x2 = 14.33333333 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 = 14.33333333 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 14.33333333 + 0.0625 Combine like terms: 14.33333333 + 0.0625 = 14.39583333 0.0625 + -0.5x + x2 = 14.39583333 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 14.39583333 Calculate the square root of the right side: 3.794184146 Break this problem into two subproblems by setting (x + -0.25) equal to 3.794184146 and -3.794184146.Subproblem 1
x + -0.25 = 3.794184146 Simplifying x + -0.25 = 3.794184146 Reorder the terms: -0.25 + x = 3.794184146 Solving -0.25 + x = 3.794184146 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 = 3.794184146 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.794184146 + 0.25 x = 3.794184146 + 0.25 Combine like terms: 3.794184146 + 0.25 = 4.044184146 x = 4.044184146 Simplifying x = 4.044184146Subproblem 2
x + -0.25 = -3.794184146 Simplifying x + -0.25 = -3.794184146 Reorder the terms: -0.25 + x = -3.794184146 Solving -0.25 + x = -3.794184146 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 = -3.794184146 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.794184146 + 0.25 x = -3.794184146 + 0.25 Combine like terms: -3.794184146 + 0.25 = -3.544184146 x = -3.544184146 Simplifying x = -3.544184146Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.044184146, -3.544184146}
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