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Simplifying 4x2 + -2x + -27 = 0 Reorder the terms: -27 + -2x + 4x2 = 0 Solving -27 + -2x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.75 + -0.5x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + -0.5x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + -0.5x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + -0.5x + x2 = 0 + 6.75 -0.5x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 -0.5x + x2 = 6.75 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 = 6.75 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 6.75 + 0.0625 Combine like terms: 6.75 + 0.0625 = 6.8125 0.0625 + -0.5x + x2 = 6.8125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 6.8125 Calculate the square root of the right side: 2.610076627 Break this problem into two subproblems by setting (x + -0.25) equal to 2.610076627 and -2.610076627.Subproblem 1
x + -0.25 = 2.610076627 Simplifying x + -0.25 = 2.610076627 Reorder the terms: -0.25 + x = 2.610076627 Solving -0.25 + x = 2.610076627 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 = 2.610076627 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.610076627 + 0.25 x = 2.610076627 + 0.25 Combine like terms: 2.610076627 + 0.25 = 2.860076627 x = 2.860076627 Simplifying x = 2.860076627Subproblem 2
x + -0.25 = -2.610076627 Simplifying x + -0.25 = -2.610076627 Reorder the terms: -0.25 + x = -2.610076627 Solving -0.25 + x = -2.610076627 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 = -2.610076627 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.610076627 + 0.25 x = -2.610076627 + 0.25 Combine like terms: -2.610076627 + 0.25 = -2.360076627 x = -2.360076627 Simplifying x = -2.360076627Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.860076627, -2.360076627}
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