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Simplifying (x + 54)(x + 49) = 85 Reorder the terms: (54 + x)(x + 49) = 85 Reorder the terms: (54 + x)(49 + x) = 85 Multiply (54 + x) * (49 + x) (54(49 + x) + x(49 + x)) = 85 ((49 * 54 + x * 54) + x(49 + x)) = 85 ((2646 + 54x) + x(49 + x)) = 85 (2646 + 54x + (49 * x + x * x)) = 85 (2646 + 54x + (49x + x2)) = 85 Combine like terms: 54x + 49x = 103x (2646 + 103x + x2) = 85 Solving 2646 + 103x + x2 = 85 Solving for variable 'x'. Reorder the terms: 2646 + -85 + 103x + x2 = 85 + -85 Combine like terms: 2646 + -85 = 2561 2561 + 103x + x2 = 85 + -85 Combine like terms: 85 + -85 = 0 2561 + 103x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2561' to each side of the equation. 2561 + 103x + -2561 + x2 = 0 + -2561 Reorder the terms: 2561 + -2561 + 103x + x2 = 0 + -2561 Combine like terms: 2561 + -2561 = 0 0 + 103x + x2 = 0 + -2561 103x + x2 = 0 + -2561 Combine like terms: 0 + -2561 = -2561 103x + x2 = -2561 The x term is 103x. Take half its coefficient (51.5). Square it (2652.25) and add it to both sides. Add '2652.25' to each side of the equation. 103x + 2652.25 + x2 = -2561 + 2652.25 Reorder the terms: 2652.25 + 103x + x2 = -2561 + 2652.25 Combine like terms: -2561 + 2652.25 = 91.25 2652.25 + 103x + x2 = 91.25 Factor a perfect square on the left side: (x + 51.5)(x + 51.5) = 91.25 Calculate the square root of the right side: 9.552486587 Break this problem into two subproblems by setting (x + 51.5) equal to 9.552486587 and -9.552486587.Subproblem 1
x + 51.5 = 9.552486587 Simplifying x + 51.5 = 9.552486587 Reorder the terms: 51.5 + x = 9.552486587 Solving 51.5 + x = 9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-51.5' to each side of the equation. 51.5 + -51.5 + x = 9.552486587 + -51.5 Combine like terms: 51.5 + -51.5 = 0.0 0.0 + x = 9.552486587 + -51.5 x = 9.552486587 + -51.5 Combine like terms: 9.552486587 + -51.5 = -41.947513413 x = -41.947513413 Simplifying x = -41.947513413Subproblem 2
x + 51.5 = -9.552486587 Simplifying x + 51.5 = -9.552486587 Reorder the terms: 51.5 + x = -9.552486587 Solving 51.5 + x = -9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-51.5' to each side of the equation. 51.5 + -51.5 + x = -9.552486587 + -51.5 Combine like terms: 51.5 + -51.5 = 0.0 0.0 + x = -9.552486587 + -51.5 x = -9.552486587 + -51.5 Combine like terms: -9.552486587 + -51.5 = -61.052486587 x = -61.052486587 Simplifying x = -61.052486587Solution
The solution to the problem is based on the solutions from the subproblems. x = {-41.947513413, -61.052486587}
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