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Simplifying 5300 = x(2650 + -1x) 5300 = (2650 * x + -1x * x) 5300 = (2650x + -1x2) Solving 5300 = 2650x + -1x2 Solving for variable 'x'. Reorder the terms: 5300 + -2650x + x2 = 2650x + -2650x + -1x2 + x2 Combine like terms: 2650x + -2650x = 0 5300 + -2650x + x2 = 0 + -1x2 + x2 5300 + -2650x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 5300 + -2650x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5300' to each side of the equation. 5300 + -2650x + -5300 + x2 = 0 + -5300 Reorder the terms: 5300 + -5300 + -2650x + x2 = 0 + -5300 Combine like terms: 5300 + -5300 = 0 0 + -2650x + x2 = 0 + -5300 -2650x + x2 = 0 + -5300 Combine like terms: 0 + -5300 = -5300 -2650x + x2 = -5300 The x term is -2650x. Take half its coefficient (-1325). Square it (1755625) and add it to both sides. Add '1755625' to each side of the equation. -2650x + 1755625 + x2 = -5300 + 1755625 Reorder the terms: 1755625 + -2650x + x2 = -5300 + 1755625 Combine like terms: -5300 + 1755625 = 1750325 1755625 + -2650x + x2 = 1750325 Factor a perfect square on the left side: (x + -1325)(x + -1325) = 1750325 Calculate the square root of the right side: 1322.998488283 Break this problem into two subproblems by setting (x + -1325) equal to 1322.998488283 and -1322.998488283.Subproblem 1
x + -1325 = 1322.998488283 Simplifying x + -1325 = 1322.998488283 Reorder the terms: -1325 + x = 1322.998488283 Solving -1325 + x = 1322.998488283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1325' to each side of the equation. -1325 + 1325 + x = 1322.998488283 + 1325 Combine like terms: -1325 + 1325 = 0 0 + x = 1322.998488283 + 1325 x = 1322.998488283 + 1325 Combine like terms: 1322.998488283 + 1325 = 2647.998488283 x = 2647.998488283 Simplifying x = 2647.998488283Subproblem 2
x + -1325 = -1322.998488283 Simplifying x + -1325 = -1322.998488283 Reorder the terms: -1325 + x = -1322.998488283 Solving -1325 + x = -1322.998488283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1325' to each side of the equation. -1325 + 1325 + x = -1322.998488283 + 1325 Combine like terms: -1325 + 1325 = 0 0 + x = -1322.998488283 + 1325 x = -1322.998488283 + 1325 Combine like terms: -1322.998488283 + 1325 = 2.001511717 x = 2.001511717 Simplifying x = 2.001511717Solution
The solution to the problem is based on the solutions from the subproblems. x = {2647.998488283, 2.001511717}
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