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Simplifying 23423 = x2 + 35x + 30 Reorder the terms: 23423 = 30 + 35x + x2 Solving 23423 = 30 + 35x + x2 Solving for variable 'x'. Combine like terms: 23423 + -30 = 23393 23393 + -35x + -1x2 = 30 + 35x + x2 + -30 + -35x + -1x2 Reorder the terms: 23393 + -35x + -1x2 = 30 + -30 + 35x + -35x + x2 + -1x2 Combine like terms: 30 + -30 = 0 23393 + -35x + -1x2 = 0 + 35x + -35x + x2 + -1x2 23393 + -35x + -1x2 = 35x + -35x + x2 + -1x2 Combine like terms: 35x + -35x = 0 23393 + -35x + -1x2 = 0 + x2 + -1x2 23393 + -35x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 23393 + -35x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -23393 + 35x + x2 = 0 Move the constant term to the right: Add '23393' to each side of the equation. -23393 + 35x + 23393 + x2 = 0 + 23393 Reorder the terms: -23393 + 23393 + 35x + x2 = 0 + 23393 Combine like terms: -23393 + 23393 = 0 0 + 35x + x2 = 0 + 23393 35x + x2 = 0 + 23393 Combine like terms: 0 + 23393 = 23393 35x + x2 = 23393 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = 23393 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 23393 + 306.25 Combine like terms: 23393 + 306.25 = 23699.25 306.25 + 35x + x2 = 23699.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 23699.25 Calculate the square root of the right side: 153.945607277 Break this problem into two subproblems by setting (x + 17.5) equal to 153.945607277 and -153.945607277.Subproblem 1
x + 17.5 = 153.945607277 Simplifying x + 17.5 = 153.945607277 Reorder the terms: 17.5 + x = 153.945607277 Solving 17.5 + x = 153.945607277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 153.945607277 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 153.945607277 + -17.5 x = 153.945607277 + -17.5 Combine like terms: 153.945607277 + -17.5 = 136.445607277 x = 136.445607277 Simplifying x = 136.445607277Subproblem 2
x + 17.5 = -153.945607277 Simplifying x + 17.5 = -153.945607277 Reorder the terms: 17.5 + x = -153.945607277 Solving 17.5 + x = -153.945607277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -153.945607277 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -153.945607277 + -17.5 x = -153.945607277 + -17.5 Combine like terms: -153.945607277 + -17.5 = -171.445607277 x = -171.445607277 Simplifying x = -171.445607277Solution
The solution to the problem is based on the solutions from the subproblems. x = {136.445607277, -171.445607277}
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