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Simplifying 9x2 + -2x + -224 = 0 Reorder the terms: -224 + -2x + 9x2 = 0 Solving -224 + -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'. -24.88888889 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '24.88888889' to each side of the equation. -24.88888889 + -0.2222222222x + 24.88888889 + x2 = 0 + 24.88888889 Reorder the terms: -24.88888889 + 24.88888889 + -0.2222222222x + x2 = 0 + 24.88888889 Combine like terms: -24.88888889 + 24.88888889 = 0.00000000 0.00000000 + -0.2222222222x + x2 = 0 + 24.88888889 -0.2222222222x + x2 = 0 + 24.88888889 Combine like terms: 0 + 24.88888889 = 24.88888889 -0.2222222222x + x2 = 24.88888889 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 = 24.88888889 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 24.88888889 + 0.01234567901 Combine like terms: 24.88888889 + 0.01234567901 = 24.90123456901 0.01234567901 + -0.2222222222x + x2 = 24.90123456901 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 24.90123456901 Calculate the square root of the right side: 4.990113683 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 4.990113683 and -4.990113683.Subproblem 1
x + -0.1111111111 = 4.990113683 Simplifying x + -0.1111111111 = 4.990113683 Reorder the terms: -0.1111111111 + x = 4.990113683 Solving -0.1111111111 + x = 4.990113683 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 = 4.990113683 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 4.990113683 + 0.1111111111 x = 4.990113683 + 0.1111111111 Combine like terms: 4.990113683 + 0.1111111111 = 5.1012247941 x = 5.1012247941 Simplifying x = 5.1012247941Subproblem 2
x + -0.1111111111 = -4.990113683 Simplifying x + -0.1111111111 = -4.990113683 Reorder the terms: -0.1111111111 + x = -4.990113683 Solving -0.1111111111 + x = -4.990113683 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 = -4.990113683 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -4.990113683 + 0.1111111111 x = -4.990113683 + 0.1111111111 Combine like terms: -4.990113683 + 0.1111111111 = -4.8790025719 x = -4.8790025719 Simplifying x = -4.8790025719Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.1012247941, -4.8790025719}
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