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Simplifying x2 + 289x + 5184 = 0 Reorder the terms: 5184 + 289x + x2 = 0 Solving 5184 + 289x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5184' to each side of the equation. 5184 + 289x + -5184 + x2 = 0 + -5184 Reorder the terms: 5184 + -5184 + 289x + x2 = 0 + -5184 Combine like terms: 5184 + -5184 = 0 0 + 289x + x2 = 0 + -5184 289x + x2 = 0 + -5184 Combine like terms: 0 + -5184 = -5184 289x + x2 = -5184 The x term is 289x. Take half its coefficient (144.5). Square it (20880.25) and add it to both sides. Add '20880.25' to each side of the equation. 289x + 20880.25 + x2 = -5184 + 20880.25 Reorder the terms: 20880.25 + 289x + x2 = -5184 + 20880.25 Combine like terms: -5184 + 20880.25 = 15696.25 20880.25 + 289x + x2 = 15696.25 Factor a perfect square on the left side: (x + 144.5)(x + 144.5) = 15696.25 Calculate the square root of the right side: 125.284675839 Break this problem into two subproblems by setting (x + 144.5) equal to 125.284675839 and -125.284675839.Subproblem 1
x + 144.5 = 125.284675839 Simplifying x + 144.5 = 125.284675839 Reorder the terms: 144.5 + x = 125.284675839 Solving 144.5 + x = 125.284675839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-144.5' to each side of the equation. 144.5 + -144.5 + x = 125.284675839 + -144.5 Combine like terms: 144.5 + -144.5 = 0.0 0.0 + x = 125.284675839 + -144.5 x = 125.284675839 + -144.5 Combine like terms: 125.284675839 + -144.5 = -19.215324161 x = -19.215324161 Simplifying x = -19.215324161Subproblem 2
x + 144.5 = -125.284675839 Simplifying x + 144.5 = -125.284675839 Reorder the terms: 144.5 + x = -125.284675839 Solving 144.5 + x = -125.284675839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-144.5' to each side of the equation. 144.5 + -144.5 + x = -125.284675839 + -144.5 Combine like terms: 144.5 + -144.5 = 0.0 0.0 + x = -125.284675839 + -144.5 x = -125.284675839 + -144.5 Combine like terms: -125.284675839 + -144.5 = -269.784675839 x = -269.784675839 Simplifying x = -269.784675839Solution
The solution to the problem is based on the solutions from the subproblems. x = {-19.215324161, -269.784675839}
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