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Simplifying x2 + -90x + -100 = 0 Reorder the terms: -100 + -90x + x2 = 0 Solving -100 + -90x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -90x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -90x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -90x + x2 = 0 + 100 -90x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -90x + x2 = 100 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 = 100 + 2025 Reorder the terms: 2025 + -90x + x2 = 100 + 2025 Combine like terms: 100 + 2025 = 2125 2025 + -90x + x2 = 2125 Factor a perfect square on the left side: (x + -45)(x + -45) = 2125 Calculate the square root of the right side: 46.097722286 Break this problem into two subproblems by setting (x + -45) equal to 46.097722286 and -46.097722286.Subproblem 1
x + -45 = 46.097722286 Simplifying x + -45 = 46.097722286 Reorder the terms: -45 + x = 46.097722286 Solving -45 + x = 46.097722286 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 = 46.097722286 + 45 Combine like terms: -45 + 45 = 0 0 + x = 46.097722286 + 45 x = 46.097722286 + 45 Combine like terms: 46.097722286 + 45 = 91.097722286 x = 91.097722286 Simplifying x = 91.097722286Subproblem 2
x + -45 = -46.097722286 Simplifying x + -45 = -46.097722286 Reorder the terms: -45 + x = -46.097722286 Solving -45 + x = -46.097722286 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 = -46.097722286 + 45 Combine like terms: -45 + 45 = 0 0 + x = -46.097722286 + 45 x = -46.097722286 + 45 Combine like terms: -46.097722286 + 45 = -1.097722286 x = -1.097722286 Simplifying x = -1.097722286Solution
The solution to the problem is based on the solutions from the subproblems. x = {91.097722286, -1.097722286}
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