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Simplifying 420 + -4800x + -1x2 = 0 Solving 420 + -4800x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -420 + 4800x + x2 = 0 Move the constant term to the right: Add '420' to each side of the equation. -420 + 4800x + 420 + x2 = 0 + 420 Reorder the terms: -420 + 420 + 4800x + x2 = 0 + 420 Combine like terms: -420 + 420 = 0 0 + 4800x + x2 = 0 + 420 4800x + x2 = 0 + 420 Combine like terms: 0 + 420 = 420 4800x + x2 = 420 The x term is 4800x. Take half its coefficient (2400). Square it (5760000) and add it to both sides. Add '5760000' to each side of the equation. 4800x + 5760000 + x2 = 420 + 5760000 Reorder the terms: 5760000 + 4800x + x2 = 420 + 5760000 Combine like terms: 420 + 5760000 = 5760420 5760000 + 4800x + x2 = 5760420 Factor a perfect square on the left side: (x + 2400)(x + 2400) = 5760420 Calculate the square root of the right side: 2400.087498405 Break this problem into two subproblems by setting (x + 2400) equal to 2400.087498405 and -2400.087498405.Subproblem 1
x + 2400 = 2400.087498405 Simplifying x + 2400 = 2400.087498405 Reorder the terms: 2400 + x = 2400.087498405 Solving 2400 + x = 2400.087498405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2400' to each side of the equation. 2400 + -2400 + x = 2400.087498405 + -2400 Combine like terms: 2400 + -2400 = 0 0 + x = 2400.087498405 + -2400 x = 2400.087498405 + -2400 Combine like terms: 2400.087498405 + -2400 = 0.087498405 x = 0.087498405 Simplifying x = 0.087498405Subproblem 2
x + 2400 = -2400.087498405 Simplifying x + 2400 = -2400.087498405 Reorder the terms: 2400 + x = -2400.087498405 Solving 2400 + x = -2400.087498405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2400' to each side of the equation. 2400 + -2400 + x = -2400.087498405 + -2400 Combine like terms: 2400 + -2400 = 0 0 + x = -2400.087498405 + -2400 x = -2400.087498405 + -2400 Combine like terms: -2400.087498405 + -2400 = -4800.087498405 x = -4800.087498405 Simplifying x = -4800.087498405Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.087498405, -4800.087498405}
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