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Simplifying 90x + -1x2 = 100 Solving 90x + -1x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 90x + -1x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 90x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 100 + -90x + x2 = 0 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 = 1925 2025 + -90x + x2 = 1925 Factor a perfect square on the left side: (x + -45)(x + -45) = 1925 Calculate the square root of the right side: 43.874821937 Break this problem into two subproblems by setting (x + -45) equal to 43.874821937 and -43.874821937.Subproblem 1
x + -45 = 43.874821937 Simplifying x + -45 = 43.874821937 Reorder the terms: -45 + x = 43.874821937 Solving -45 + x = 43.874821937 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 = 43.874821937 + 45 Combine like terms: -45 + 45 = 0 0 + x = 43.874821937 + 45 x = 43.874821937 + 45 Combine like terms: 43.874821937 + 45 = 88.874821937 x = 88.874821937 Simplifying x = 88.874821937Subproblem 2
x + -45 = -43.874821937 Simplifying x + -45 = -43.874821937 Reorder the terms: -45 + x = -43.874821937 Solving -45 + x = -43.874821937 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 = -43.874821937 + 45 Combine like terms: -45 + 45 = 0 0 + x = -43.874821937 + 45 x = -43.874821937 + 45 Combine like terms: -43.874821937 + 45 = 1.125178063 x = 1.125178063 Simplifying x = 1.125178063Solution
The solution to the problem is based on the solutions from the subproblems. x = {88.874821937, 1.125178063}
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