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Simplifying 9x2 + 36x + 31 = 0 Reorder the terms: 31 + 36x + 9x2 = 0 Solving 31 + 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'. 3.444444444 + 4x + x2 = 0 Move the constant term to the right: Add '-3.444444444' to each side of the equation. 3.444444444 + 4x + -3.444444444 + x2 = 0 + -3.444444444 Reorder the terms: 3.444444444 + -3.444444444 + 4x + x2 = 0 + -3.444444444 Combine like terms: 3.444444444 + -3.444444444 = 0.000000000 0.000000000 + 4x + x2 = 0 + -3.444444444 4x + x2 = 0 + -3.444444444 Combine like terms: 0 + -3.444444444 = -3.444444444 4x + x2 = -3.444444444 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 = -3.444444444 + 4 Reorder the terms: 4 + 4x + x2 = -3.444444444 + 4 Combine like terms: -3.444444444 + 4 = 0.555555556 4 + 4x + x2 = 0.555555556 Factor a perfect square on the left side: (x + 2)(x + 2) = 0.555555556 Calculate the square root of the right side: 0.745355993 Break this problem into two subproblems by setting (x + 2) equal to 0.745355993 and -0.745355993.Subproblem 1
x + 2 = 0.745355993 Simplifying x + 2 = 0.745355993 Reorder the terms: 2 + x = 0.745355993 Solving 2 + x = 0.745355993 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 = 0.745355993 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.745355993 + -2 x = 0.745355993 + -2 Combine like terms: 0.745355993 + -2 = -1.254644007 x = -1.254644007 Simplifying x = -1.254644007Subproblem 2
x + 2 = -0.745355993 Simplifying x + 2 = -0.745355993 Reorder the terms: 2 + x = -0.745355993 Solving 2 + x = -0.745355993 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 = -0.745355993 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.745355993 + -2 x = -0.745355993 + -2 Combine like terms: -0.745355993 + -2 = -2.745355993 x = -2.745355993 Simplifying x = -2.745355993Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.254644007, -2.745355993}
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