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Simplifying 276 = 23x + x2 Solving 276 = 23x + x2 Solving for variable 'x'. Reorder the terms: 276 + -23x + -1x2 = 23x + -23x + x2 + -1x2 Combine like terms: 23x + -23x = 0 276 + -23x + -1x2 = 0 + x2 + -1x2 276 + -23x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 276 + -23x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -276 + 23x + x2 = 0 Move the constant term to the right: Add '276' to each side of the equation. -276 + 23x + 276 + x2 = 0 + 276 Reorder the terms: -276 + 276 + 23x + x2 = 0 + 276 Combine like terms: -276 + 276 = 0 0 + 23x + x2 = 0 + 276 23x + x2 = 0 + 276 Combine like terms: 0 + 276 = 276 23x + x2 = 276 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = 276 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 276 + 132.25 Combine like terms: 276 + 132.25 = 408.25 132.25 + 23x + x2 = 408.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 408.25 Calculate the square root of the right side: 20.205197351 Break this problem into two subproblems by setting (x + 11.5) equal to 20.205197351 and -20.205197351.Subproblem 1
x + 11.5 = 20.205197351 Simplifying x + 11.5 = 20.205197351 Reorder the terms: 11.5 + x = 20.205197351 Solving 11.5 + x = 20.205197351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 20.205197351 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 20.205197351 + -11.5 x = 20.205197351 + -11.5 Combine like terms: 20.205197351 + -11.5 = 8.705197351 x = 8.705197351 Simplifying x = 8.705197351Subproblem 2
x + 11.5 = -20.205197351 Simplifying x + 11.5 = -20.205197351 Reorder the terms: 11.5 + x = -20.205197351 Solving 11.5 + x = -20.205197351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -20.205197351 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -20.205197351 + -11.5 x = -20.205197351 + -11.5 Combine like terms: -20.205197351 + -11.5 = -31.705197351 x = -31.705197351 Simplifying x = -31.705197351Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.705197351, -31.705197351}
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