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Simplifying 9x + -0.83x2 = 22 Solving 9x + -0.83x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + 9x + -0.83x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + 9x + -0.83x2 = 0 Begin completing the square. Divide all terms by -0.83 the coefficient of the squared term: Divide each side by '-0.83'. 26.5060241 + -10.84337349x + x2 = 0 Move the constant term to the right: Add '-26.5060241' to each side of the equation. 26.5060241 + -10.84337349x + -26.5060241 + x2 = 0 + -26.5060241 Reorder the terms: 26.5060241 + -26.5060241 + -10.84337349x + x2 = 0 + -26.5060241 Combine like terms: 26.5060241 + -26.5060241 = 0.0000000 0.0000000 + -10.84337349x + x2 = 0 + -26.5060241 -10.84337349x + x2 = 0 + -26.5060241 Combine like terms: 0 + -26.5060241 = -26.5060241 -10.84337349x + x2 = -26.5060241 The x term is -10.84337349x. Take half its coefficient (-5.421686745). Square it (29.39468716) and add it to both sides. Add '29.39468716' to each side of the equation. -10.84337349x + 29.39468716 + x2 = -26.5060241 + 29.39468716 Reorder the terms: 29.39468716 + -10.84337349x + x2 = -26.5060241 + 29.39468716 Combine like terms: -26.5060241 + 29.39468716 = 2.88866306 29.39468716 + -10.84337349x + x2 = 2.88866306 Factor a perfect square on the left side: (x + -5.421686745)(x + -5.421686745) = 2.88866306 Calculate the square root of the right side: 1.699606737 Break this problem into two subproblems by setting (x + -5.421686745) equal to 1.699606737 and -1.699606737.Subproblem 1
x + -5.421686745 = 1.699606737 Simplifying x + -5.421686745 = 1.699606737 Reorder the terms: -5.421686745 + x = 1.699606737 Solving -5.421686745 + x = 1.699606737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.421686745' to each side of the equation. -5.421686745 + 5.421686745 + x = 1.699606737 + 5.421686745 Combine like terms: -5.421686745 + 5.421686745 = 0.000000000 0.000000000 + x = 1.699606737 + 5.421686745 x = 1.699606737 + 5.421686745 Combine like terms: 1.699606737 + 5.421686745 = 7.121293482 x = 7.121293482 Simplifying x = 7.121293482Subproblem 2
x + -5.421686745 = -1.699606737 Simplifying x + -5.421686745 = -1.699606737 Reorder the terms: -5.421686745 + x = -1.699606737 Solving -5.421686745 + x = -1.699606737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.421686745' to each side of the equation. -5.421686745 + 5.421686745 + x = -1.699606737 + 5.421686745 Combine like terms: -5.421686745 + 5.421686745 = 0.000000000 0.000000000 + x = -1.699606737 + 5.421686745 x = -1.699606737 + 5.421686745 Combine like terms: -1.699606737 + 5.421686745 = 3.722080008 x = 3.722080008 Simplifying x = 3.722080008Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.121293482, 3.722080008}
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