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Simplifying x2 + 1200x = 360000 Reorder the terms: 1200x + x2 = 360000 Solving 1200x + x2 = 360000 Solving for variable 'x'. Reorder the terms: -360000 + 1200x + x2 = 360000 + -360000 Combine like terms: 360000 + -360000 = 0 -360000 + 1200x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '360000' to each side of the equation. -360000 + 1200x + 360000 + x2 = 0 + 360000 Reorder the terms: -360000 + 360000 + 1200x + x2 = 0 + 360000 Combine like terms: -360000 + 360000 = 0 0 + 1200x + x2 = 0 + 360000 1200x + x2 = 0 + 360000 Combine like terms: 0 + 360000 = 360000 1200x + x2 = 360000 The x term is 1200x. Take half its coefficient (600). Square it (360000) and add it to both sides. Add '360000' to each side of the equation. 1200x + 360000 + x2 = 360000 + 360000 Reorder the terms: 360000 + 1200x + x2 = 360000 + 360000 Combine like terms: 360000 + 360000 = 720000 360000 + 1200x + x2 = 720000 Factor a perfect square on the left side: (x + 600)(x + 600) = 720000 Calculate the square root of the right side: 848.528137424 Break this problem into two subproblems by setting (x + 600) equal to 848.528137424 and -848.528137424.Subproblem 1
x + 600 = 848.528137424 Simplifying x + 600 = 848.528137424 Reorder the terms: 600 + x = 848.528137424 Solving 600 + x = 848.528137424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-600' to each side of the equation. 600 + -600 + x = 848.528137424 + -600 Combine like terms: 600 + -600 = 0 0 + x = 848.528137424 + -600 x = 848.528137424 + -600 Combine like terms: 848.528137424 + -600 = 248.528137424 x = 248.528137424 Simplifying x = 248.528137424Subproblem 2
x + 600 = -848.528137424 Simplifying x + 600 = -848.528137424 Reorder the terms: 600 + x = -848.528137424 Solving 600 + x = -848.528137424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-600' to each side of the equation. 600 + -600 + x = -848.528137424 + -600 Combine like terms: 600 + -600 = 0 0 + x = -848.528137424 + -600 x = -848.528137424 + -600 Combine like terms: -848.528137424 + -600 = -1448.528137424 x = -1448.528137424 Simplifying x = -1448.528137424Solution
The solution to the problem is based on the solutions from the subproblems. x = {248.528137424, -1448.528137424}
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