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Simplifying 4x2 + -22 = 11x Reorder the terms: -22 + 4x2 = 11x Solving -22 + 4x2 = 11x Solving for variable 'x'. Reorder the terms: -22 + -11x + 4x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -22 + -11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.5 + -2.75x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -2.75x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -2.75x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -2.75x + x2 = 0 + 5.5 -2.75x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -2.75x + x2 = 5.5 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 5.5 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 5.5 + 1.890625 Combine like terms: 5.5 + 1.890625 = 7.390625 1.890625 + -2.75x + x2 = 7.390625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 7.390625 Calculate the square root of the right side: 2.718570396 Break this problem into two subproblems by setting (x + -1.375) equal to 2.718570396 and -2.718570396.Subproblem 1
x + -1.375 = 2.718570396 Simplifying x + -1.375 = 2.718570396 Reorder the terms: -1.375 + x = 2.718570396 Solving -1.375 + x = 2.718570396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 2.718570396 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.718570396 + 1.375 x = 2.718570396 + 1.375 Combine like terms: 2.718570396 + 1.375 = 4.093570396 x = 4.093570396 Simplifying x = 4.093570396Subproblem 2
x + -1.375 = -2.718570396 Simplifying x + -1.375 = -2.718570396 Reorder the terms: -1.375 + x = -2.718570396 Solving -1.375 + x = -2.718570396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -2.718570396 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.718570396 + 1.375 x = -2.718570396 + 1.375 Combine like terms: -2.718570396 + 1.375 = -1.343570396 x = -1.343570396 Simplifying x = -1.343570396Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.093570396, -1.343570396}
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