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Simplifying 121 = 9x + x2 Solving 121 = 9x + x2 Solving for variable 'x'. Reorder the terms: 121 + -9x + -1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 121 + -9x + -1x2 = 0 + x2 + -1x2 121 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 121 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -121 + 9x + x2 = 0 Move the constant term to the right: Add '121' to each side of the equation. -121 + 9x + 121 + x2 = 0 + 121 Reorder the terms: -121 + 121 + 9x + x2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + 9x + x2 = 0 + 121 9x + x2 = 0 + 121 Combine like terms: 0 + 121 = 121 9x + x2 = 121 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 121 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 121 + 20.25 Combine like terms: 121 + 20.25 = 141.25 20.25 + 9x + x2 = 141.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 141.25 Calculate the square root of the right side: 11.884864324 Break this problem into two subproblems by setting (x + 4.5) equal to 11.884864324 and -11.884864324.Subproblem 1
x + 4.5 = 11.884864324 Simplifying x + 4.5 = 11.884864324 Reorder the terms: 4.5 + x = 11.884864324 Solving 4.5 + x = 11.884864324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 11.884864324 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 11.884864324 + -4.5 x = 11.884864324 + -4.5 Combine like terms: 11.884864324 + -4.5 = 7.384864324 x = 7.384864324 Simplifying x = 7.384864324Subproblem 2
x + 4.5 = -11.884864324 Simplifying x + 4.5 = -11.884864324 Reorder the terms: 4.5 + x = -11.884864324 Solving 4.5 + x = -11.884864324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -11.884864324 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -11.884864324 + -4.5 x = -11.884864324 + -4.5 Combine like terms: -11.884864324 + -4.5 = -16.384864324 x = -16.384864324 Simplifying x = -16.384864324Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.384864324, -16.384864324}
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