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Simplifying 4x2 + -22x = 9 Reorder the terms: -22x + 4x2 = 9 Solving -22x + 4x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -22x + 4x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -22x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -5.5x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -5.5x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -5.5x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -5.5x + x2 = 0 + 2.25 -5.5x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -5.5x + x2 = 2.25 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 2.25 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 2.25 + 7.5625 Combine like terms: 2.25 + 7.5625 = 9.8125 7.5625 + -5.5x + x2 = 9.8125 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 9.8125 Calculate the square root of the right side: 3.132491022 Break this problem into two subproblems by setting (x + -2.75) equal to 3.132491022 and -3.132491022.Subproblem 1
x + -2.75 = 3.132491022 Simplifying x + -2.75 = 3.132491022 Reorder the terms: -2.75 + x = 3.132491022 Solving -2.75 + x = 3.132491022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 3.132491022 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.132491022 + 2.75 x = 3.132491022 + 2.75 Combine like terms: 3.132491022 + 2.75 = 5.882491022 x = 5.882491022 Simplifying x = 5.882491022Subproblem 2
x + -2.75 = -3.132491022 Simplifying x + -2.75 = -3.132491022 Reorder the terms: -2.75 + x = -3.132491022 Solving -2.75 + x = -3.132491022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -3.132491022 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.132491022 + 2.75 x = -3.132491022 + 2.75 Combine like terms: -3.132491022 + 2.75 = -0.382491022 x = -0.382491022 Simplifying x = -0.382491022Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.882491022, -0.382491022}
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