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Simplifying x2 + -560x + 5600 = 0 Reorder the terms: 5600 + -560x + x2 = 0 Solving 5600 + -560x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5600' to each side of the equation. 5600 + -560x + -5600 + x2 = 0 + -5600 Reorder the terms: 5600 + -5600 + -560x + x2 = 0 + -5600 Combine like terms: 5600 + -5600 = 0 0 + -560x + x2 = 0 + -5600 -560x + x2 = 0 + -5600 Combine like terms: 0 + -5600 = -5600 -560x + x2 = -5600 The x term is -560x. Take half its coefficient (-280). Square it (78400) and add it to both sides. Add '78400' to each side of the equation. -560x + 78400 + x2 = -5600 + 78400 Reorder the terms: 78400 + -560x + x2 = -5600 + 78400 Combine like terms: -5600 + 78400 = 72800 78400 + -560x + x2 = 72800 Factor a perfect square on the left side: (x + -280)(x + -280) = 72800 Calculate the square root of the right side: 269.814751265 Break this problem into two subproblems by setting (x + -280) equal to 269.814751265 and -269.814751265.Subproblem 1
x + -280 = 269.814751265 Simplifying x + -280 = 269.814751265 Reorder the terms: -280 + x = 269.814751265 Solving -280 + x = 269.814751265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '280' to each side of the equation. -280 + 280 + x = 269.814751265 + 280 Combine like terms: -280 + 280 = 0 0 + x = 269.814751265 + 280 x = 269.814751265 + 280 Combine like terms: 269.814751265 + 280 = 549.814751265 x = 549.814751265 Simplifying x = 549.814751265Subproblem 2
x + -280 = -269.814751265 Simplifying x + -280 = -269.814751265 Reorder the terms: -280 + x = -269.814751265 Solving -280 + x = -269.814751265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '280' to each side of the equation. -280 + 280 + x = -269.814751265 + 280 Combine like terms: -280 + 280 = 0 0 + x = -269.814751265 + 280 x = -269.814751265 + 280 Combine like terms: -269.814751265 + 280 = 10.185248735 x = 10.185248735 Simplifying x = 10.185248735Solution
The solution to the problem is based on the solutions from the subproblems. x = {549.814751265, 10.185248735}
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