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Simplifying x2 + 144x + 54 = 0 Reorder the terms: 54 + 144x + x2 = 0 Solving 54 + 144x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + 144x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + 144x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + 144x + x2 = 0 + -54 144x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 144x + x2 = -54 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 = -54 + 5184 Reorder the terms: 5184 + 144x + x2 = -54 + 5184 Combine like terms: -54 + 5184 = 5130 5184 + 144x + x2 = 5130 Factor a perfect square on the left side: (x + 72)(x + 72) = 5130 Calculate the square root of the right side: 71.624018318 Break this problem into two subproblems by setting (x + 72) equal to 71.624018318 and -71.624018318.Subproblem 1
x + 72 = 71.624018318 Simplifying x + 72 = 71.624018318 Reorder the terms: 72 + x = 71.624018318 Solving 72 + x = 71.624018318 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 = 71.624018318 + -72 Combine like terms: 72 + -72 = 0 0 + x = 71.624018318 + -72 x = 71.624018318 + -72 Combine like terms: 71.624018318 + -72 = -0.375981682 x = -0.375981682 Simplifying x = -0.375981682Subproblem 2
x + 72 = -71.624018318 Simplifying x + 72 = -71.624018318 Reorder the terms: 72 + x = -71.624018318 Solving 72 + x = -71.624018318 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 = -71.624018318 + -72 Combine like terms: 72 + -72 = 0 0 + x = -71.624018318 + -72 x = -71.624018318 + -72 Combine like terms: -71.624018318 + -72 = -143.624018318 x = -143.624018318 Simplifying x = -143.624018318Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.375981682, -143.624018318}
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