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Simplifying 9x2 + -2x + -26 = 0 Reorder the terms: -26 + -2x + 9x2 = 0 Solving -26 + -2x + 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'. -2.888888889 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '2.888888889' to each side of the equation. -2.888888889 + -0.2222222222x + 2.888888889 + x2 = 0 + 2.888888889 Reorder the terms: -2.888888889 + 2.888888889 + -0.2222222222x + x2 = 0 + 2.888888889 Combine like terms: -2.888888889 + 2.888888889 = 0.000000000 0.000000000 + -0.2222222222x + x2 = 0 + 2.888888889 -0.2222222222x + x2 = 0 + 2.888888889 Combine like terms: 0 + 2.888888889 = 2.888888889 -0.2222222222x + x2 = 2.888888889 The x term is -0.2222222222x. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222x + 0.01234567901 + x2 = 2.888888889 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 2.888888889 + 0.01234567901 Combine like terms: 2.888888889 + 0.01234567901 = 2.90123456801 0.01234567901 + -0.2222222222x + x2 = 2.90123456801 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 2.90123456801 Calculate the square root of the right side: 1.70330108 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 1.70330108 and -1.70330108.Subproblem 1
x + -0.1111111111 = 1.70330108 Simplifying x + -0.1111111111 = 1.70330108 Reorder the terms: -0.1111111111 + x = 1.70330108 Solving -0.1111111111 + x = 1.70330108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = 1.70330108 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 1.70330108 + 0.1111111111 x = 1.70330108 + 0.1111111111 Combine like terms: 1.70330108 + 0.1111111111 = 1.8144121911 x = 1.8144121911 Simplifying x = 1.8144121911Subproblem 2
x + -0.1111111111 = -1.70330108 Simplifying x + -0.1111111111 = -1.70330108 Reorder the terms: -0.1111111111 + x = -1.70330108 Solving -0.1111111111 + x = -1.70330108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = -1.70330108 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -1.70330108 + 0.1111111111 x = -1.70330108 + 0.1111111111 Combine like terms: -1.70330108 + 0.1111111111 = -1.5921899689 x = -1.5921899689 Simplifying x = -1.5921899689Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8144121911, -1.5921899689}
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