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Simplifying (x2) + -580x + 15000 = 0 x2 + -580x + 15000 = 0 Reorder the terms: 15000 + -580x + x2 = 0 Solving 15000 + -580x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15000' to each side of the equation. 15000 + -580x + -15000 + x2 = 0 + -15000 Reorder the terms: 15000 + -15000 + -580x + x2 = 0 + -15000 Combine like terms: 15000 + -15000 = 0 0 + -580x + x2 = 0 + -15000 -580x + x2 = 0 + -15000 Combine like terms: 0 + -15000 = -15000 -580x + x2 = -15000 The x term is -580x. Take half its coefficient (-290). Square it (84100) and add it to both sides. Add '84100' to each side of the equation. -580x + 84100 + x2 = -15000 + 84100 Reorder the terms: 84100 + -580x + x2 = -15000 + 84100 Combine like terms: -15000 + 84100 = 69100 84100 + -580x + x2 = 69100 Factor a perfect square on the left side: (x + -290)(x + -290) = 69100 Calculate the square root of the right side: 262.868788562 Break this problem into two subproblems by setting (x + -290) equal to 262.868788562 and -262.868788562.Subproblem 1
x + -290 = 262.868788562 Simplifying x + -290 = 262.868788562 Reorder the terms: -290 + x = 262.868788562 Solving -290 + x = 262.868788562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '290' to each side of the equation. -290 + 290 + x = 262.868788562 + 290 Combine like terms: -290 + 290 = 0 0 + x = 262.868788562 + 290 x = 262.868788562 + 290 Combine like terms: 262.868788562 + 290 = 552.868788562 x = 552.868788562 Simplifying x = 552.868788562Subproblem 2
x + -290 = -262.868788562 Simplifying x + -290 = -262.868788562 Reorder the terms: -290 + x = -262.868788562 Solving -290 + x = -262.868788562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '290' to each side of the equation. -290 + 290 + x = -262.868788562 + 290 Combine like terms: -290 + 290 = 0 0 + x = -262.868788562 + 290 x = -262.868788562 + 290 Combine like terms: -262.868788562 + 290 = 27.131211438 x = 27.131211438 Simplifying x = 27.131211438Solution
The solution to the problem is based on the solutions from the subproblems. x = {552.868788562, 27.131211438}
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