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Simplifying 9x2 + -36x + 1 = 0 Reorder the terms: 1 + -36x + 9x2 = 0 Solving 1 + -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'. 0.1111111111 + -4x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + -4x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + -4x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + -0.1111111111 -4x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 -4x + x2 = -0.1111111111 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 = -0.1111111111 + 4 Reorder the terms: 4 + -4x + x2 = -0.1111111111 + 4 Combine like terms: -0.1111111111 + 4 = 3.8888888889 4 + -4x + x2 = 3.8888888889 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.8888888889 Calculate the square root of the right side: 1.972026594 Break this problem into two subproblems by setting (x + -2) equal to 1.972026594 and -1.972026594.Subproblem 1
x + -2 = 1.972026594 Simplifying x + -2 = 1.972026594 Reorder the terms: -2 + x = 1.972026594 Solving -2 + x = 1.972026594 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 = 1.972026594 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.972026594 + 2 x = 1.972026594 + 2 Combine like terms: 1.972026594 + 2 = 3.972026594 x = 3.972026594 Simplifying x = 3.972026594Subproblem 2
x + -2 = -1.972026594 Simplifying x + -2 = -1.972026594 Reorder the terms: -2 + x = -1.972026594 Solving -2 + x = -1.972026594 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 = -1.972026594 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.972026594 + 2 x = -1.972026594 + 2 Combine like terms: -1.972026594 + 2 = 0.027973406 x = 0.027973406 Simplifying x = 0.027973406Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.972026594, 0.027973406}
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