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Simplifying 4x2 + 2 + -1x + -48 = 0 Reorder the terms: 2 + -48 + -1x + 4x2 = 0 Combine like terms: 2 + -48 = -46 -46 + -1x + 4x2 = 0 Solving -46 + -1x + 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'. -11.5 + -0.25x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -0.25x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -0.25x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -0.25x + x2 = 0 + 11.5 -0.25x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -0.25x + x2 = 11.5 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 11.5 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 11.5 + 0.015625 Combine like terms: 11.5 + 0.015625 = 11.515625 0.015625 + -0.25x + x2 = 11.515625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 11.515625 Calculate the square root of the right side: 3.39346799 Break this problem into two subproblems by setting (x + -0.125) equal to 3.39346799 and -3.39346799.Subproblem 1
x + -0.125 = 3.39346799 Simplifying x + -0.125 = 3.39346799 Reorder the terms: -0.125 + x = 3.39346799 Solving -0.125 + x = 3.39346799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 3.39346799 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 3.39346799 + 0.125 x = 3.39346799 + 0.125 Combine like terms: 3.39346799 + 0.125 = 3.51846799 x = 3.51846799 Simplifying x = 3.51846799Subproblem 2
x + -0.125 = -3.39346799 Simplifying x + -0.125 = -3.39346799 Reorder the terms: -0.125 + x = -3.39346799 Solving -0.125 + x = -3.39346799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -3.39346799 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -3.39346799 + 0.125 x = -3.39346799 + 0.125 Combine like terms: -3.39346799 + 0.125 = -3.26846799 x = -3.26846799 Simplifying x = -3.26846799Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.51846799, -3.26846799}
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