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Simplifying x2 + 15x = 2000 Reorder the terms: 15x + x2 = 2000 Solving 15x + x2 = 2000 Solving for variable 'x'. Reorder the terms: -2000 + 15x + x2 = 2000 + -2000 Combine like terms: 2000 + -2000 = 0 -2000 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2000' to each side of the equation. -2000 + 15x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + 15x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + 15x + x2 = 0 + 2000 15x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 15x + x2 = 2000 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 2000 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 2000 + 56.25 Combine like terms: 2000 + 56.25 = 2056.25 56.25 + 15x + x2 = 2056.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 2056.25 Calculate the square root of the right side: 45.345892868 Break this problem into two subproblems by setting (x + 7.5) equal to 45.345892868 and -45.345892868.Subproblem 1
x + 7.5 = 45.345892868 Simplifying x + 7.5 = 45.345892868 Reorder the terms: 7.5 + x = 45.345892868 Solving 7.5 + x = 45.345892868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 45.345892868 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 45.345892868 + -7.5 x = 45.345892868 + -7.5 Combine like terms: 45.345892868 + -7.5 = 37.845892868 x = 37.845892868 Simplifying x = 37.845892868Subproblem 2
x + 7.5 = -45.345892868 Simplifying x + 7.5 = -45.345892868 Reorder the terms: 7.5 + x = -45.345892868 Solving 7.5 + x = -45.345892868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -45.345892868 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -45.345892868 + -7.5 x = -45.345892868 + -7.5 Combine like terms: -45.345892868 + -7.5 = -52.845892868 x = -52.845892868 Simplifying x = -52.845892868Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.845892868, -52.845892868}
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