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Simplifying 11x2 + -37x + -4 = 0 Reorder the terms: -4 + -37x + 11x2 = 0 Solving -4 + -37x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.3636363636 + -3.363636364x + x2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + -3.363636364x + 0.3636363636 + x2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + -3.363636364x + x2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + -3.363636364x + x2 = 0 + 0.3636363636 -3.363636364x + x2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 -3.363636364x + x2 = 0.3636363636 The x term is -3.363636364x. Take half its coefficient (-1.681818182). Square it (2.828512397) and add it to both sides. Add '2.828512397' to each side of the equation. -3.363636364x + 2.828512397 + x2 = 0.3636363636 + 2.828512397 Reorder the terms: 2.828512397 + -3.363636364x + x2 = 0.3636363636 + 2.828512397 Combine like terms: 0.3636363636 + 2.828512397 = 3.1921487606 2.828512397 + -3.363636364x + x2 = 3.1921487606 Factor a perfect square on the left side: (x + -1.681818182)(x + -1.681818182) = 3.1921487606 Calculate the square root of the right side: 1.786658546 Break this problem into two subproblems by setting (x + -1.681818182) equal to 1.786658546 and -1.786658546.Subproblem 1
x + -1.681818182 = 1.786658546 Simplifying x + -1.681818182 = 1.786658546 Reorder the terms: -1.681818182 + x = 1.786658546 Solving -1.681818182 + x = 1.786658546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.681818182' to each side of the equation. -1.681818182 + 1.681818182 + x = 1.786658546 + 1.681818182 Combine like terms: -1.681818182 + 1.681818182 = 0.000000000 0.000000000 + x = 1.786658546 + 1.681818182 x = 1.786658546 + 1.681818182 Combine like terms: 1.786658546 + 1.681818182 = 3.468476728 x = 3.468476728 Simplifying x = 3.468476728Subproblem 2
x + -1.681818182 = -1.786658546 Simplifying x + -1.681818182 = -1.786658546 Reorder the terms: -1.681818182 + x = -1.786658546 Solving -1.681818182 + x = -1.786658546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.681818182' to each side of the equation. -1.681818182 + 1.681818182 + x = -1.786658546 + 1.681818182 Combine like terms: -1.681818182 + 1.681818182 = 0.000000000 0.000000000 + x = -1.786658546 + 1.681818182 x = -1.786658546 + 1.681818182 Combine like terms: -1.786658546 + 1.681818182 = -0.104840364 x = -0.104840364 Simplifying x = -0.104840364Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.468476728, -0.104840364}
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