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Simplifying x2 + -90x + -450 = 0 Reorder the terms: -450 + -90x + x2 = 0 Solving -450 + -90x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '450' to each side of the equation. -450 + -90x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + -90x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + -90x + x2 = 0 + 450 -90x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 -90x + x2 = 450 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 = 450 + 2025 Reorder the terms: 2025 + -90x + x2 = 450 + 2025 Combine like terms: 450 + 2025 = 2475 2025 + -90x + x2 = 2475 Factor a perfect square on the left side: (x + -45)(x + -45) = 2475 Calculate the square root of the right side: 49.749371855 Break this problem into two subproblems by setting (x + -45) equal to 49.749371855 and -49.749371855.Subproblem 1
x + -45 = 49.749371855 Simplifying x + -45 = 49.749371855 Reorder the terms: -45 + x = 49.749371855 Solving -45 + x = 49.749371855 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 = 49.749371855 + 45 Combine like terms: -45 + 45 = 0 0 + x = 49.749371855 + 45 x = 49.749371855 + 45 Combine like terms: 49.749371855 + 45 = 94.749371855 x = 94.749371855 Simplifying x = 94.749371855Subproblem 2
x + -45 = -49.749371855 Simplifying x + -45 = -49.749371855 Reorder the terms: -45 + x = -49.749371855 Solving -45 + x = -49.749371855 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 = -49.749371855 + 45 Combine like terms: -45 + 45 = 0 0 + x = -49.749371855 + 45 x = -49.749371855 + 45 Combine like terms: -49.749371855 + 45 = -4.749371855 x = -4.749371855 Simplifying x = -4.749371855Solution
The solution to the problem is based on the solutions from the subproblems. x = {94.749371855, -4.749371855}
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