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Simplifying x2 + -81x + -8503056 = 0 Reorder the terms: -8503056 + -81x + x2 = 0 Solving -8503056 + -81x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8503056' to each side of the equation. -8503056 + -81x + 8503056 + x2 = 0 + 8503056 Reorder the terms: -8503056 + 8503056 + -81x + x2 = 0 + 8503056 Combine like terms: -8503056 + 8503056 = 0 0 + -81x + x2 = 0 + 8503056 -81x + x2 = 0 + 8503056 Combine like terms: 0 + 8503056 = 8503056 -81x + x2 = 8503056 The x term is -81x. Take half its coefficient (-40.5). Square it (1640.25) and add it to both sides. Add '1640.25' to each side of the equation. -81x + 1640.25 + x2 = 8503056 + 1640.25 Reorder the terms: 1640.25 + -81x + x2 = 8503056 + 1640.25 Combine like terms: 8503056 + 1640.25 = 8504696.25 1640.25 + -81x + x2 = 8504696.25 Factor a perfect square on the left side: (x + -40.5)(x + -40.5) = 8504696.25 Calculate the square root of the right side: 2916.281236438 Break this problem into two subproblems by setting (x + -40.5) equal to 2916.281236438 and -2916.281236438.Subproblem 1
x + -40.5 = 2916.281236438 Simplifying x + -40.5 = 2916.281236438 Reorder the terms: -40.5 + x = 2916.281236438 Solving -40.5 + x = 2916.281236438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + x = 2916.281236438 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = 2916.281236438 + 40.5 x = 2916.281236438 + 40.5 Combine like terms: 2916.281236438 + 40.5 = 2956.781236438 x = 2956.781236438 Simplifying x = 2956.781236438Subproblem 2
x + -40.5 = -2916.281236438 Simplifying x + -40.5 = -2916.281236438 Reorder the terms: -40.5 + x = -2916.281236438 Solving -40.5 + x = -2916.281236438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + x = -2916.281236438 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = -2916.281236438 + 40.5 x = -2916.281236438 + 40.5 Combine like terms: -2916.281236438 + 40.5 = -2875.781236438 x = -2875.781236438 Simplifying x = -2875.781236438Solution
The solution to the problem is based on the solutions from the subproblems. x = {2956.781236438, -2875.781236438}
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