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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 = 2.745355993 x = 2.745355993 Simplifying x = 2.745355993Subproblem 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 = 1.254644007 x = 1.254644007 Simplifying x = 1.254644007Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.745355993, 1.254644007}
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