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Simplifying 169 + x2 + -39x = 0 Reorder the terms: 169 + -39x + x2 = 0 Solving 169 + -39x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-169' to each side of the equation. 169 + -39x + -169 + x2 = 0 + -169 Reorder the terms: 169 + -169 + -39x + x2 = 0 + -169 Combine like terms: 169 + -169 = 0 0 + -39x + x2 = 0 + -169 -39x + x2 = 0 + -169 Combine like terms: 0 + -169 = -169 -39x + x2 = -169 The x term is -39x. Take half its coefficient (-19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. -39x + 380.25 + x2 = -169 + 380.25 Reorder the terms: 380.25 + -39x + x2 = -169 + 380.25 Combine like terms: -169 + 380.25 = 211.25 380.25 + -39x + x2 = 211.25 Factor a perfect square on the left side: (x + -19.5)(x + -19.5) = 211.25 Calculate the square root of the right side: 14.534441854 Break this problem into two subproblems by setting (x + -19.5) equal to 14.534441854 and -14.534441854.Subproblem 1
x + -19.5 = 14.534441854 Simplifying x + -19.5 = 14.534441854 Reorder the terms: -19.5 + x = 14.534441854 Solving -19.5 + x = 14.534441854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = 14.534441854 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = 14.534441854 + 19.5 x = 14.534441854 + 19.5 Combine like terms: 14.534441854 + 19.5 = 34.034441854 x = 34.034441854 Simplifying x = 34.034441854Subproblem 2
x + -19.5 = -14.534441854 Simplifying x + -19.5 = -14.534441854 Reorder the terms: -19.5 + x = -14.534441854 Solving -19.5 + x = -14.534441854 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = -14.534441854 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = -14.534441854 + 19.5 x = -14.534441854 + 19.5 Combine like terms: -14.534441854 + 19.5 = 4.965558146 x = 4.965558146 Simplifying x = 4.965558146Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.034441854, 4.965558146}
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