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Simplifying 9x2 + 36x + -46 = 0 Reorder the terms: -46 + 36x + 9x2 = 0 Solving -46 + 36x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5.111111111 + 4x + x2 = 0 Move the constant term to the right: Add '5.111111111' to each side of the equation. -5.111111111 + 4x + 5.111111111 + x2 = 0 + 5.111111111 Reorder the terms: -5.111111111 + 5.111111111 + 4x + x2 = 0 + 5.111111111 Combine like terms: -5.111111111 + 5.111111111 = 0.000000000 0.000000000 + 4x + x2 = 0 + 5.111111111 4x + x2 = 0 + 5.111111111 Combine like terms: 0 + 5.111111111 = 5.111111111 4x + x2 = 5.111111111 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 = 5.111111111 + 4 Reorder the terms: 4 + 4x + x2 = 5.111111111 + 4 Combine like terms: 5.111111111 + 4 = 9.111111111 4 + 4x + x2 = 9.111111111 Factor a perfect square on the left side: (x + 2)(x + 2) = 9.111111111 Calculate the square root of the right side: 3.018461713 Break this problem into two subproblems by setting (x + 2) equal to 3.018461713 and -3.018461713.Subproblem 1
x + 2 = 3.018461713 Simplifying x + 2 = 3.018461713 Reorder the terms: 2 + x = 3.018461713 Solving 2 + x = 3.018461713 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 = 3.018461713 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.018461713 + -2 x = 3.018461713 + -2 Combine like terms: 3.018461713 + -2 = 1.018461713 x = 1.018461713 Simplifying x = 1.018461713Subproblem 2
x + 2 = -3.018461713 Simplifying x + 2 = -3.018461713 Reorder the terms: 2 + x = -3.018461713 Solving 2 + x = -3.018461713 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 = -3.018461713 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.018461713 + -2 x = -3.018461713 + -2 Combine like terms: -3.018461713 + -2 = -5.018461713 x = -5.018461713 Simplifying x = -5.018461713Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.018461713, -5.018461713}
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