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Simplifying 0 = 3600 + -1x2 + -10x + 25 Reorder the terms: 0 = 3600 + 25 + -10x + -1x2 Combine like terms: 3600 + 25 = 3625 0 = 3625 + -10x + -1x2 Solving 0 = 3625 + -10x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -3625 = -3625 -3625 + 10x + x2 = 3625 + -10x + -1x2 + -3625 + 10x + x2 Reorder the terms: -3625 + 10x + x2 = 3625 + -3625 + -10x + 10x + -1x2 + x2 Combine like terms: 3625 + -3625 = 0 -3625 + 10x + x2 = 0 + -10x + 10x + -1x2 + x2 -3625 + 10x + x2 = -10x + 10x + -1x2 + x2 Combine like terms: -10x + 10x = 0 -3625 + 10x + x2 = 0 + -1x2 + x2 -3625 + 10x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -3625 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3625' to each side of the equation. -3625 + 10x + 3625 + x2 = 0 + 3625 Reorder the terms: -3625 + 3625 + 10x + x2 = 0 + 3625 Combine like terms: -3625 + 3625 = 0 0 + 10x + x2 = 0 + 3625 10x + x2 = 0 + 3625 Combine like terms: 0 + 3625 = 3625 10x + x2 = 3625 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 3625 + 25 Reorder the terms: 25 + 10x + x2 = 3625 + 25 Combine like terms: 3625 + 25 = 3650 25 + 10x + x2 = 3650 Factor a perfect square on the left side: (x + 5)(x + 5) = 3650 Calculate the square root of the right side: 60.415229868 Break this problem into two subproblems by setting (x + 5) equal to 60.415229868 and -60.415229868.Subproblem 1
x + 5 = 60.415229868 Simplifying x + 5 = 60.415229868 Reorder the terms: 5 + x = 60.415229868 Solving 5 + x = 60.415229868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 60.415229868 + -5 Combine like terms: 5 + -5 = 0 0 + x = 60.415229868 + -5 x = 60.415229868 + -5 Combine like terms: 60.415229868 + -5 = 55.415229868 x = 55.415229868 Simplifying x = 55.415229868Subproblem 2
x + 5 = -60.415229868 Simplifying x + 5 = -60.415229868 Reorder the terms: 5 + x = -60.415229868 Solving 5 + x = -60.415229868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -60.415229868 + -5 Combine like terms: 5 + -5 = 0 0 + x = -60.415229868 + -5 x = -60.415229868 + -5 Combine like terms: -60.415229868 + -5 = -65.415229868 x = -65.415229868 Simplifying x = -65.415229868Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.415229868, -65.415229868}
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