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Simplifying 9x2 + -1200x + 5440 = 0 Reorder the terms: 5440 + -1200x + 9x2 = 0 Solving 5440 + -1200x + 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'. 604.4444444 + -133.3333333x + x2 = 0 Move the constant term to the right: Add '-604.4444444' to each side of the equation. 604.4444444 + -133.3333333x + -604.4444444 + x2 = 0 + -604.4444444 Reorder the terms: 604.4444444 + -604.4444444 + -133.3333333x + x2 = 0 + -604.4444444 Combine like terms: 604.4444444 + -604.4444444 = 0.0000000 0.0000000 + -133.3333333x + x2 = 0 + -604.4444444 -133.3333333x + x2 = 0 + -604.4444444 Combine like terms: 0 + -604.4444444 = -604.4444444 -133.3333333x + x2 = -604.4444444 The x term is -133.3333333x. Take half its coefficient (-66.66666665). Square it (4444.444442) and add it to both sides. Add '4444.444442' to each side of the equation. -133.3333333x + 4444.444442 + x2 = -604.4444444 + 4444.444442 Reorder the terms: 4444.444442 + -133.3333333x + x2 = -604.4444444 + 4444.444442 Combine like terms: -604.4444444 + 4444.444442 = 3839.9999976 4444.444442 + -133.3333333x + x2 = 3839.9999976 Factor a perfect square on the left side: (x + -66.66666665)(x + -66.66666665) = 3839.9999976 Calculate the square root of the right side: 61.96773352 Break this problem into two subproblems by setting (x + -66.66666665) equal to 61.96773352 and -61.96773352.Subproblem 1
x + -66.66666665 = 61.96773352 Simplifying x + -66.66666665 = 61.96773352 Reorder the terms: -66.66666665 + x = 61.96773352 Solving -66.66666665 + x = 61.96773352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.66666665' to each side of the equation. -66.66666665 + 66.66666665 + x = 61.96773352 + 66.66666665 Combine like terms: -66.66666665 + 66.66666665 = 0.00000000 0.00000000 + x = 61.96773352 + 66.66666665 x = 61.96773352 + 66.66666665 Combine like terms: 61.96773352 + 66.66666665 = 128.63440017 x = 128.63440017 Simplifying x = 128.63440017Subproblem 2
x + -66.66666665 = -61.96773352 Simplifying x + -66.66666665 = -61.96773352 Reorder the terms: -66.66666665 + x = -61.96773352 Solving -66.66666665 + x = -61.96773352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.66666665' to each side of the equation. -66.66666665 + 66.66666665 + x = -61.96773352 + 66.66666665 Combine like terms: -66.66666665 + 66.66666665 = 0.00000000 0.00000000 + x = -61.96773352 + 66.66666665 x = -61.96773352 + 66.66666665 Combine like terms: -61.96773352 + 66.66666665 = 4.69893313 x = 4.69893313 Simplifying x = 4.69893313Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.63440017, 4.69893313}
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