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Simplifying 13x + 273 = x2 + 52 Reorder the terms: 273 + 13x = x2 + 52 Reorder the terms: 273 + 13x = 52 + x2 Solving 273 + 13x = 52 + x2 Solving for variable 'x'. Reorder the terms: 273 + -52 + 13x + -1x2 = 52 + x2 + -52 + -1x2 Combine like terms: 273 + -52 = 221 221 + 13x + -1x2 = 52 + x2 + -52 + -1x2 Reorder the terms: 221 + 13x + -1x2 = 52 + -52 + x2 + -1x2 Combine like terms: 52 + -52 = 0 221 + 13x + -1x2 = 0 + x2 + -1x2 221 + 13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 221 + 13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -221 + -13x + x2 = 0 Move the constant term to the right: Add '221' to each side of the equation. -221 + -13x + 221 + x2 = 0 + 221 Reorder the terms: -221 + 221 + -13x + x2 = 0 + 221 Combine like terms: -221 + 221 = 0 0 + -13x + x2 = 0 + 221 -13x + x2 = 0 + 221 Combine like terms: 0 + 221 = 221 -13x + x2 = 221 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 221 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 221 + 42.25 Combine like terms: 221 + 42.25 = 263.25 42.25 + -13x + x2 = 263.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 263.25 Calculate the square root of the right side: 16.22498074 Break this problem into two subproblems by setting (x + -6.5) equal to 16.22498074 and -16.22498074.Subproblem 1
x + -6.5 = 16.22498074 Simplifying x + -6.5 = 16.22498074 Reorder the terms: -6.5 + x = 16.22498074 Solving -6.5 + x = 16.22498074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 16.22498074 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 16.22498074 + 6.5 x = 16.22498074 + 6.5 Combine like terms: 16.22498074 + 6.5 = 22.72498074 x = 22.72498074 Simplifying x = 22.72498074Subproblem 2
x + -6.5 = -16.22498074 Simplifying x + -6.5 = -16.22498074 Reorder the terms: -6.5 + x = -16.22498074 Solving -6.5 + x = -16.22498074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -16.22498074 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -16.22498074 + 6.5 x = -16.22498074 + 6.5 Combine like terms: -16.22498074 + 6.5 = -9.72498074 x = -9.72498074 Simplifying x = -9.72498074Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.72498074, -9.72498074}
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