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Simplifying 13x + x2 = 169 Solving 13x + x2 = 169 Solving for variable 'x'. Reorder the terms: -169 + 13x + x2 = 169 + -169 Combine like terms: 169 + -169 = 0 -169 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '169' to each side of the equation. -169 + 13x + 169 + x2 = 0 + 169 Reorder the terms: -169 + 169 + 13x + x2 = 0 + 169 Combine like terms: -169 + 169 = 0 0 + 13x + x2 = 0 + 169 13x + x2 = 0 + 169 Combine like terms: 0 + 169 = 169 13x + x2 = 169 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 = 169 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 169 + 42.25 Combine like terms: 169 + 42.25 = 211.25 42.25 + 13x + x2 = 211.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 211.25 Calculate the square root of the right side: 14.534441854 Break this problem into two subproblems by setting (x + 6.5) equal to 14.534441854 and -14.534441854.Subproblem 1
x + 6.5 = 14.534441854 Simplifying x + 6.5 = 14.534441854 Reorder the terms: 6.5 + x = 14.534441854 Solving 6.5 + x = 14.534441854 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 = 14.534441854 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 14.534441854 + -6.5 x = 14.534441854 + -6.5 Combine like terms: 14.534441854 + -6.5 = 8.034441854 x = 8.034441854 Simplifying x = 8.034441854Subproblem 2
x + 6.5 = -14.534441854 Simplifying x + 6.5 = -14.534441854 Reorder the terms: 6.5 + x = -14.534441854 Solving 6.5 + x = -14.534441854 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 = -14.534441854 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -14.534441854 + -6.5 x = -14.534441854 + -6.5 Combine like terms: -14.534441854 + -6.5 = -21.034441854 x = -21.034441854 Simplifying x = -21.034441854Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.034441854, -21.034441854}
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