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Simplifying 13x + x2 = 100 Solving 13x + x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 13x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 13x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 13x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 13x + x2 = 0 + 100 13x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 13x + x2 = 100 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 = 100 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 100 + 42.25 Combine like terms: 100 + 42.25 = 142.25 42.25 + 13x + x2 = 142.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 142.25 Calculate the square root of the right side: 11.926860442 Break this problem into two subproblems by setting (x + 6.5) equal to 11.926860442 and -11.926860442.Subproblem 1
x + 6.5 = 11.926860442 Simplifying x + 6.5 = 11.926860442 Reorder the terms: 6.5 + x = 11.926860442 Solving 6.5 + x = 11.926860442 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 = 11.926860442 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 11.926860442 + -6.5 x = 11.926860442 + -6.5 Combine like terms: 11.926860442 + -6.5 = 5.426860442 x = 5.426860442 Simplifying x = 5.426860442Subproblem 2
x + 6.5 = -11.926860442 Simplifying x + 6.5 = -11.926860442 Reorder the terms: 6.5 + x = -11.926860442 Solving 6.5 + x = -11.926860442 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 = -11.926860442 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -11.926860442 + -6.5 x = -11.926860442 + -6.5 Combine like terms: -11.926860442 + -6.5 = -18.426860442 x = -18.426860442 Simplifying x = -18.426860442Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.426860442, -18.426860442}
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