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Simplifying -11x2 + 35x + 260 = 0 Reorder the terms: 260 + 35x + -11x2 = 0 Solving 260 + 35x + -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'. -23.63636364 + -3.181818182x + x2 = 0 Move the constant term to the right: Add '23.63636364' to each side of the equation. -23.63636364 + -3.181818182x + 23.63636364 + x2 = 0 + 23.63636364 Reorder the terms: -23.63636364 + 23.63636364 + -3.181818182x + x2 = 0 + 23.63636364 Combine like terms: -23.63636364 + 23.63636364 = 0.00000000 0.00000000 + -3.181818182x + x2 = 0 + 23.63636364 -3.181818182x + x2 = 0 + 23.63636364 Combine like terms: 0 + 23.63636364 = 23.63636364 -3.181818182x + x2 = 23.63636364 The x term is -3.181818182x. Take half its coefficient (-1.590909091). Square it (2.530991736) and add it to both sides. Add '2.530991736' to each side of the equation. -3.181818182x + 2.530991736 + x2 = 23.63636364 + 2.530991736 Reorder the terms: 2.530991736 + -3.181818182x + x2 = 23.63636364 + 2.530991736 Combine like terms: 23.63636364 + 2.530991736 = 26.167355376 2.530991736 + -3.181818182x + x2 = 26.167355376 Factor a perfect square on the left side: (x + -1.590909091)(x + -1.590909091) = 26.167355376 Calculate the square root of the right side: 5.115403735 Break this problem into two subproblems by setting (x + -1.590909091) equal to 5.115403735 and -5.115403735.Subproblem 1
x + -1.590909091 = 5.115403735 Simplifying x + -1.590909091 = 5.115403735 Reorder the terms: -1.590909091 + x = 5.115403735 Solving -1.590909091 + x = 5.115403735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.590909091' to each side of the equation. -1.590909091 + 1.590909091 + x = 5.115403735 + 1.590909091 Combine like terms: -1.590909091 + 1.590909091 = 0.000000000 0.000000000 + x = 5.115403735 + 1.590909091 x = 5.115403735 + 1.590909091 Combine like terms: 5.115403735 + 1.590909091 = 6.706312826 x = 6.706312826 Simplifying x = 6.706312826Subproblem 2
x + -1.590909091 = -5.115403735 Simplifying x + -1.590909091 = -5.115403735 Reorder the terms: -1.590909091 + x = -5.115403735 Solving -1.590909091 + x = -5.115403735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.590909091' to each side of the equation. -1.590909091 + 1.590909091 + x = -5.115403735 + 1.590909091 Combine like terms: -1.590909091 + 1.590909091 = 0.000000000 0.000000000 + x = -5.115403735 + 1.590909091 x = -5.115403735 + 1.590909091 Combine like terms: -5.115403735 + 1.590909091 = -3.524494644 x = -3.524494644 Simplifying x = -3.524494644Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.706312826, -3.524494644}
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