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Simplifying 4x2 + -2x = 55 Reorder the terms: -2x + 4x2 = 55 Solving -2x + 4x2 = 55 Solving for variable 'x'. Reorder the terms: -55 + -2x + 4x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + -2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.75 + -0.5x + x2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + -0.5x + 13.75 + x2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + -0.5x + x2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + -0.5x + x2 = 0 + 13.75 -0.5x + x2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 -0.5x + x2 = 13.75 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 = 13.75 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 13.75 + 0.0625 Combine like terms: 13.75 + 0.0625 = 13.8125 0.0625 + -0.5x + x2 = 13.8125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 13.8125 Calculate the square root of the right side: 3.716517187 Break this problem into two subproblems by setting (x + -0.25) equal to 3.716517187 and -3.716517187.Subproblem 1
x + -0.25 = 3.716517187 Simplifying x + -0.25 = 3.716517187 Reorder the terms: -0.25 + x = 3.716517187 Solving -0.25 + x = 3.716517187 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 = 3.716517187 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.716517187 + 0.25 x = 3.716517187 + 0.25 Combine like terms: 3.716517187 + 0.25 = 3.966517187 x = 3.966517187 Simplifying x = 3.966517187Subproblem 2
x + -0.25 = -3.716517187 Simplifying x + -0.25 = -3.716517187 Reorder the terms: -0.25 + x = -3.716517187 Solving -0.25 + x = -3.716517187 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 = -3.716517187 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.716517187 + 0.25 x = -3.716517187 + 0.25 Combine like terms: -3.716517187 + 0.25 = -3.466517187 x = -3.466517187 Simplifying x = -3.466517187Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.966517187, -3.466517187}
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