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Simplifying -9x2 + 36x = -41 Reorder the terms: 36x + -9x2 = -41 Solving 36x + -9x2 = -41 Solving for variable 'x'. Reorder the terms: 41 + 36x + -9x2 = -41 + 41 Combine like terms: -41 + 41 = 0 41 + 36x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -4.555555556 + -4x + x2 = 0 Move the constant term to the right: Add '4.555555556' to each side of the equation. -4.555555556 + -4x + 4.555555556 + x2 = 0 + 4.555555556 Reorder the terms: -4.555555556 + 4.555555556 + -4x + x2 = 0 + 4.555555556 Combine like terms: -4.555555556 + 4.555555556 = 0.000000000 0.000000000 + -4x + x2 = 0 + 4.555555556 -4x + x2 = 0 + 4.555555556 Combine like terms: 0 + 4.555555556 = 4.555555556 -4x + x2 = 4.555555556 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 4.555555556 + 4 Reorder the terms: 4 + -4x + x2 = 4.555555556 + 4 Combine like terms: 4.555555556 + 4 = 8.555555556 4 + -4x + x2 = 8.555555556 Factor a perfect square on the left side: (x + -2)(x + -2) = 8.555555556 Calculate the square root of the right side: 2.924988129 Break this problem into two subproblems by setting (x + -2) equal to 2.924988129 and -2.924988129.Subproblem 1
x + -2 = 2.924988129 Simplifying x + -2 = 2.924988129 Reorder the terms: -2 + x = 2.924988129 Solving -2 + x = 2.924988129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.924988129 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.924988129 + 2 x = 2.924988129 + 2 Combine like terms: 2.924988129 + 2 = 4.924988129 x = 4.924988129 Simplifying x = 4.924988129Subproblem 2
x + -2 = -2.924988129 Simplifying x + -2 = -2.924988129 Reorder the terms: -2 + x = -2.924988129 Solving -2 + x = -2.924988129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.924988129 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.924988129 + 2 x = -2.924988129 + 2 Combine like terms: -2.924988129 + 2 = -0.924988129 x = -0.924988129 Simplifying x = -0.924988129Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.924988129, -0.924988129}
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