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Simplifying 9x2 + -36x + 5 = 0 Reorder the terms: 5 + -36x + 9x2 = 0 Solving 5 + -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'. 0.5555555556 + -4x + x2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + -4x + -0.5555555556 + x2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + -4x + x2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + -0.5555555556 -4x + x2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 -4x + x2 = -0.5555555556 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 = -0.5555555556 + 4 Reorder the terms: 4 + -4x + x2 = -0.5555555556 + 4 Combine like terms: -0.5555555556 + 4 = 3.4444444444 4 + -4x + x2 = 3.4444444444 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.4444444444 Calculate the square root of the right side: 1.855921454 Break this problem into two subproblems by setting (x + -2) equal to 1.855921454 and -1.855921454.Subproblem 1
x + -2 = 1.855921454 Simplifying x + -2 = 1.855921454 Reorder the terms: -2 + x = 1.855921454 Solving -2 + x = 1.855921454 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 = 1.855921454 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.855921454 + 2 x = 1.855921454 + 2 Combine like terms: 1.855921454 + 2 = 3.855921454 x = 3.855921454 Simplifying x = 3.855921454Subproblem 2
x + -2 = -1.855921454 Simplifying x + -2 = -1.855921454 Reorder the terms: -2 + x = -1.855921454 Solving -2 + x = -1.855921454 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 = -1.855921454 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.855921454 + 2 x = -1.855921454 + 2 Combine like terms: -1.855921454 + 2 = 0.144078546 x = 0.144078546 Simplifying x = 0.144078546Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.855921454, 0.144078546}
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