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Simplifying 4x2 + -11x = 10 Reorder the terms: -11x + 4x2 = 10 Solving -11x + 4x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -11x + 4x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5 + -2.75x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -2.75x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -2.75x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -2.75x + x2 = 0 + 2.5 -2.75x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -2.75x + x2 = 2.5 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 = 2.5 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 2.5 + 1.890625 Combine like terms: 2.5 + 1.890625 = 4.390625 1.890625 + -2.75x + x2 = 4.390625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (x + -1.375) equal to 2.095381827 and -2.095381827.Subproblem 1
x + -1.375 = 2.095381827 Simplifying x + -1.375 = 2.095381827 Reorder the terms: -1.375 + x = 2.095381827 Solving -1.375 + x = 2.095381827 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 = 2.095381827 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.095381827 + 1.375 x = 2.095381827 + 1.375 Combine like terms: 2.095381827 + 1.375 = 3.470381827 x = 3.470381827 Simplifying x = 3.470381827Subproblem 2
x + -1.375 = -2.095381827 Simplifying x + -1.375 = -2.095381827 Reorder the terms: -1.375 + x = -2.095381827 Solving -1.375 + x = -2.095381827 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 = -2.095381827 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.095381827 + 1.375 x = -2.095381827 + 1.375 Combine like terms: -2.095381827 + 1.375 = -0.720381827 x = -0.720381827 Simplifying x = -0.720381827Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.470381827, -0.720381827}
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