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Simplifying x2 + 600x = 4800 Reorder the terms: 600x + x2 = 4800 Solving 600x + x2 = 4800 Solving for variable 'x'. Reorder the terms: -4800 + 600x + x2 = 4800 + -4800 Combine like terms: 4800 + -4800 = 0 -4800 + 600x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4800' to each side of the equation. -4800 + 600x + 4800 + x2 = 0 + 4800 Reorder the terms: -4800 + 4800 + 600x + x2 = 0 + 4800 Combine like terms: -4800 + 4800 = 0 0 + 600x + x2 = 0 + 4800 600x + x2 = 0 + 4800 Combine like terms: 0 + 4800 = 4800 600x + x2 = 4800 The x term is 600x. Take half its coefficient (300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. 600x + 90000 + x2 = 4800 + 90000 Reorder the terms: 90000 + 600x + x2 = 4800 + 90000 Combine like terms: 4800 + 90000 = 94800 90000 + 600x + x2 = 94800 Factor a perfect square on the left side: (x + 300)(x + 300) = 94800 Calculate the square root of the right side: 307.896086367 Break this problem into two subproblems by setting (x + 300) equal to 307.896086367 and -307.896086367.Subproblem 1
x + 300 = 307.896086367 Simplifying x + 300 = 307.896086367 Reorder the terms: 300 + x = 307.896086367 Solving 300 + x = 307.896086367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = 307.896086367 + -300 Combine like terms: 300 + -300 = 0 0 + x = 307.896086367 + -300 x = 307.896086367 + -300 Combine like terms: 307.896086367 + -300 = 7.896086367 x = 7.896086367 Simplifying x = 7.896086367Subproblem 2
x + 300 = -307.896086367 Simplifying x + 300 = -307.896086367 Reorder the terms: 300 + x = -307.896086367 Solving 300 + x = -307.896086367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = -307.896086367 + -300 Combine like terms: 300 + -300 = 0 0 + x = -307.896086367 + -300 x = -307.896086367 + -300 Combine like terms: -307.896086367 + -300 = -607.896086367 x = -607.896086367 Simplifying x = -607.896086367Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.896086367, -607.896086367}
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