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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 = 7.444444444 4 + 4x + x2 = 7.444444444 Factor a perfect square on the left side: (x + 2)(x + 2) = 7.444444444 Calculate the square root of the right side: 2.728450924 Break this problem into two subproblems by setting (x + 2) equal to 2.728450924 and -2.728450924.Subproblem 1
x + 2 = 2.728450924 Simplifying x + 2 = 2.728450924 Reorder the terms: 2 + x = 2.728450924 Solving 2 + x = 2.728450924 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 = 2.728450924 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.728450924 + -2 x = 2.728450924 + -2 Combine like terms: 2.728450924 + -2 = 0.728450924 x = 0.728450924 Simplifying x = 0.728450924Subproblem 2
x + 2 = -2.728450924 Simplifying x + 2 = -2.728450924 Reorder the terms: 2 + x = -2.728450924 Solving 2 + x = -2.728450924 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 = -2.728450924 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.728450924 + -2 x = -2.728450924 + -2 Combine like terms: -2.728450924 + -2 = -4.728450924 x = -4.728450924 Simplifying x = -4.728450924Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.728450924, -4.728450924}
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