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Simplifying 42 = 13x + x2 Solving 42 = 13x + x2 Solving for variable 'x'. Reorder the terms: 42 + -13x + -1x2 = 13x + -13x + x2 + -1x2 Combine like terms: 13x + -13x = 0 42 + -13x + -1x2 = 0 + x2 + -1x2 42 + -13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 42 + -13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -42 + 13x + x2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + 13x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 13x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 13x + x2 = 0 + 42 13x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 13x + x2 = 42 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 = 42 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 42 + 42.25 Combine like terms: 42 + 42.25 = 84.25 42.25 + 13x + x2 = 84.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (x + 6.5) equal to 9.178779875 and -9.178779875.Subproblem 1
x + 6.5 = 9.178779875 Simplifying x + 6.5 = 9.178779875 Reorder the terms: 6.5 + x = 9.178779875 Solving 6.5 + x = 9.178779875 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 = 9.178779875 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 9.178779875 + -6.5 x = 9.178779875 + -6.5 Combine like terms: 9.178779875 + -6.5 = 2.678779875 x = 2.678779875 Simplifying x = 2.678779875Subproblem 2
x + 6.5 = -9.178779875 Simplifying x + 6.5 = -9.178779875 Reorder the terms: 6.5 + x = -9.178779875 Solving 6.5 + x = -9.178779875 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 = -9.178779875 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -9.178779875 + -6.5 x = -9.178779875 + -6.5 Combine like terms: -9.178779875 + -6.5 = -15.678779875 x = -15.678779875 Simplifying x = -15.678779875Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.678779875, -15.678779875}
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