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Simplifying 2x2 + 20x + -5525 = 0 Reorder the terms: -5525 + 20x + 2x2 = 0 Solving -5525 + 20x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2762.5 + 10x + x2 = 0 Move the constant term to the right: Add '2762.5' to each side of the equation. -2762.5 + 10x + 2762.5 + x2 = 0 + 2762.5 Reorder the terms: -2762.5 + 2762.5 + 10x + x2 = 0 + 2762.5 Combine like terms: -2762.5 + 2762.5 = 0.0 0.0 + 10x + x2 = 0 + 2762.5 10x + x2 = 0 + 2762.5 Combine like terms: 0 + 2762.5 = 2762.5 10x + x2 = 2762.5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 2762.5 + 25 Reorder the terms: 25 + 10x + x2 = 2762.5 + 25 Combine like terms: 2762.5 + 25 = 2787.5 25 + 10x + x2 = 2787.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 2787.5 Calculate the square root of the right side: 52.796780205 Break this problem into two subproblems by setting (x + 5) equal to 52.796780205 and -52.796780205.Subproblem 1
x + 5 = 52.796780205 Simplifying x + 5 = 52.796780205 Reorder the terms: 5 + x = 52.796780205 Solving 5 + x = 52.796780205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 52.796780205 + -5 Combine like terms: 5 + -5 = 0 0 + x = 52.796780205 + -5 x = 52.796780205 + -5 Combine like terms: 52.796780205 + -5 = 47.796780205 x = 47.796780205 Simplifying x = 47.796780205Subproblem 2
x + 5 = -52.796780205 Simplifying x + 5 = -52.796780205 Reorder the terms: 5 + x = -52.796780205 Solving 5 + x = -52.796780205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -52.796780205 + -5 Combine like terms: 5 + -5 = 0 0 + x = -52.796780205 + -5 x = -52.796780205 + -5 Combine like terms: -52.796780205 + -5 = -57.796780205 x = -57.796780205 Simplifying x = -57.796780205Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.796780205, -57.796780205}
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