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Simplifying x2 + 90x + -2025 = 0 Reorder the terms: -2025 + 90x + x2 = 0 Solving -2025 + 90x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2025' to each side of the equation. -2025 + 90x + 2025 + x2 = 0 + 2025 Reorder the terms: -2025 + 2025 + 90x + x2 = 0 + 2025 Combine like terms: -2025 + 2025 = 0 0 + 90x + x2 = 0 + 2025 90x + x2 = 0 + 2025 Combine like terms: 0 + 2025 = 2025 90x + x2 = 2025 The x term is 90x. Take half its coefficient (45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. 90x + 2025 + x2 = 2025 + 2025 Reorder the terms: 2025 + 90x + x2 = 2025 + 2025 Combine like terms: 2025 + 2025 = 4050 2025 + 90x + x2 = 4050 Factor a perfect square on the left side: (x + 45)(x + 45) = 4050 Calculate the square root of the right side: 63.639610307 Break this problem into two subproblems by setting (x + 45) equal to 63.639610307 and -63.639610307.Subproblem 1
x + 45 = 63.639610307 Simplifying x + 45 = 63.639610307 Reorder the terms: 45 + x = 63.639610307 Solving 45 + x = 63.639610307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = 63.639610307 + -45 Combine like terms: 45 + -45 = 0 0 + x = 63.639610307 + -45 x = 63.639610307 + -45 Combine like terms: 63.639610307 + -45 = 18.639610307 x = 18.639610307 Simplifying x = 18.639610307Subproblem 2
x + 45 = -63.639610307 Simplifying x + 45 = -63.639610307 Reorder the terms: 45 + x = -63.639610307 Solving 45 + x = -63.639610307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = -63.639610307 + -45 Combine like terms: 45 + -45 = 0 0 + x = -63.639610307 + -45 x = -63.639610307 + -45 Combine like terms: -63.639610307 + -45 = -108.639610307 x = -108.639610307 Simplifying x = -108.639610307Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.639610307, -108.639610307}
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