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Simplifying 9x2 + x + -22 = 0 Reorder the terms: -22 + x + 9x2 = 0 Solving -22 + x + 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'. -2.444444444 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '2.444444444' to each side of the equation. -2.444444444 + 0.1111111111x + 2.444444444 + x2 = 0 + 2.444444444 Reorder the terms: -2.444444444 + 2.444444444 + 0.1111111111x + x2 = 0 + 2.444444444 Combine like terms: -2.444444444 + 2.444444444 = 0.000000000 0.000000000 + 0.1111111111x + x2 = 0 + 2.444444444 0.1111111111x + x2 = 0 + 2.444444444 Combine like terms: 0 + 2.444444444 = 2.444444444 0.1111111111x + x2 = 2.444444444 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1111111111x + 0.25 + x2 = 2.444444444 + 0.25 Reorder the terms: 0.25 + 0.1111111111x + x2 = 2.444444444 + 0.25 Combine like terms: 2.444444444 + 0.25 = 2.694444444 0.25 + 0.1111111111x + x2 = 2.694444444 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.694444444 Calculate the square root of the right side: 1.6414763 Break this problem into two subproblems by setting (x + 0.5) equal to 1.6414763 and -1.6414763.Subproblem 1
x + 0.5 = 1.6414763 Simplifying x + 0.5 = 1.6414763 Reorder the terms: 0.5 + x = 1.6414763 Solving 0.5 + x = 1.6414763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.6414763 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.6414763 + -0.5 x = 1.6414763 + -0.5 Combine like terms: 1.6414763 + -0.5 = 1.1414763 x = 1.1414763 Simplifying x = 1.1414763Subproblem 2
x + 0.5 = -1.6414763 Simplifying x + 0.5 = -1.6414763 Reorder the terms: 0.5 + x = -1.6414763 Solving 0.5 + x = -1.6414763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.6414763 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.6414763 + -0.5 x = -1.6414763 + -0.5 Combine like terms: -1.6414763 + -0.5 = -2.1414763 x = -2.1414763 Simplifying x = -2.1414763Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1414763, -2.1414763}
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