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Simplifying x2 + 45x = 90 Reorder the terms: 45x + x2 = 90 Solving 45x + x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 45x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 45x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 45x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 45x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 45x + x2 = 0 + 90 45x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 45x + x2 = 90 The x term is 45x. Take half its coefficient (22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. 45x + 506.25 + x2 = 90 + 506.25 Reorder the terms: 506.25 + 45x + x2 = 90 + 506.25 Combine like terms: 90 + 506.25 = 596.25 506.25 + 45x + x2 = 596.25 Factor a perfect square on the left side: (x + 22.5)(x + 22.5) = 596.25 Calculate the square root of the right side: 24.418230894 Break this problem into two subproblems by setting (x + 22.5) equal to 24.418230894 and -24.418230894.Subproblem 1
x + 22.5 = 24.418230894 Simplifying x + 22.5 = 24.418230894 Reorder the terms: 22.5 + x = 24.418230894 Solving 22.5 + x = 24.418230894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = 24.418230894 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = 24.418230894 + -22.5 x = 24.418230894 + -22.5 Combine like terms: 24.418230894 + -22.5 = 1.918230894 x = 1.918230894 Simplifying x = 1.918230894Subproblem 2
x + 22.5 = -24.418230894 Simplifying x + 22.5 = -24.418230894 Reorder the terms: 22.5 + x = -24.418230894 Solving 22.5 + x = -24.418230894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = -24.418230894 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = -24.418230894 + -22.5 x = -24.418230894 + -22.5 Combine like terms: -24.418230894 + -22.5 = -46.918230894 x = -46.918230894 Simplifying x = -46.918230894Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.918230894, -46.918230894}
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