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Simplifying x2 + 144x + 2659 = 0 Reorder the terms: 2659 + 144x + x2 = 0 Solving 2659 + 144x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2659' to each side of the equation. 2659 + 144x + -2659 + x2 = 0 + -2659 Reorder the terms: 2659 + -2659 + 144x + x2 = 0 + -2659 Combine like terms: 2659 + -2659 = 0 0 + 144x + x2 = 0 + -2659 144x + x2 = 0 + -2659 Combine like terms: 0 + -2659 = -2659 144x + x2 = -2659 The x term is 144x. Take half its coefficient (72). Square it (5184) and add it to both sides. Add '5184' to each side of the equation. 144x + 5184 + x2 = -2659 + 5184 Reorder the terms: 5184 + 144x + x2 = -2659 + 5184 Combine like terms: -2659 + 5184 = 2525 5184 + 144x + x2 = 2525 Factor a perfect square on the left side: (x + 72)(x + 72) = 2525 Calculate the square root of the right side: 50.249378106 Break this problem into two subproblems by setting (x + 72) equal to 50.249378106 and -50.249378106.Subproblem 1
x + 72 = 50.249378106 Simplifying x + 72 = 50.249378106 Reorder the terms: 72 + x = 50.249378106 Solving 72 + x = 50.249378106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-72' to each side of the equation. 72 + -72 + x = 50.249378106 + -72 Combine like terms: 72 + -72 = 0 0 + x = 50.249378106 + -72 x = 50.249378106 + -72 Combine like terms: 50.249378106 + -72 = -21.750621894 x = -21.750621894 Simplifying x = -21.750621894Subproblem 2
x + 72 = -50.249378106 Simplifying x + 72 = -50.249378106 Reorder the terms: 72 + x = -50.249378106 Solving 72 + x = -50.249378106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-72' to each side of the equation. 72 + -72 + x = -50.249378106 + -72 Combine like terms: 72 + -72 = 0 0 + x = -50.249378106 + -72 x = -50.249378106 + -72 Combine like terms: -50.249378106 + -72 = -122.249378106 x = -122.249378106 Simplifying x = -122.249378106Solution
The solution to the problem is based on the solutions from the subproblems. x = {-21.750621894, -122.249378106}
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