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Simplifying x(x + 49) = 12 Reorder the terms: x(49 + x) = 12 (49 * x + x * x) = 12 (49x + x2) = 12 Solving 49x + x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 49x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 49x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 49x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 49x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 49x + x2 = 0 + 12 49x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 49x + x2 = 12 The x term is 49x. Take half its coefficient (24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. 49x + 600.25 + x2 = 12 + 600.25 Reorder the terms: 600.25 + 49x + x2 = 12 + 600.25 Combine like terms: 12 + 600.25 = 612.25 600.25 + 49x + x2 = 612.25 Factor a perfect square on the left side: (x + 24.5)(x + 24.5) = 612.25 Calculate the square root of the right side: 24.743686063 Break this problem into two subproblems by setting (x + 24.5) equal to 24.743686063 and -24.743686063.Subproblem 1
x + 24.5 = 24.743686063 Simplifying x + 24.5 = 24.743686063 Reorder the terms: 24.5 + x = 24.743686063 Solving 24.5 + x = 24.743686063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = 24.743686063 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = 24.743686063 + -24.5 x = 24.743686063 + -24.5 Combine like terms: 24.743686063 + -24.5 = 0.243686063 x = 0.243686063 Simplifying x = 0.243686063Subproblem 2
x + 24.5 = -24.743686063 Simplifying x + 24.5 = -24.743686063 Reorder the terms: 24.5 + x = -24.743686063 Solving 24.5 + x = -24.743686063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = -24.743686063 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = -24.743686063 + -24.5 x = -24.743686063 + -24.5 Combine like terms: -24.743686063 + -24.5 = -49.243686063 x = -49.243686063 Simplifying x = -49.243686063Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.243686063, -49.243686063}
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