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Simplifying x2 + 92x + -5985 = 0 Reorder the terms: -5985 + 92x + x2 = 0 Solving -5985 + 92x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5985' to each side of the equation. -5985 + 92x + 5985 + x2 = 0 + 5985 Reorder the terms: -5985 + 5985 + 92x + x2 = 0 + 5985 Combine like terms: -5985 + 5985 = 0 0 + 92x + x2 = 0 + 5985 92x + x2 = 0 + 5985 Combine like terms: 0 + 5985 = 5985 92x + x2 = 5985 The x term is 92x. Take half its coefficient (46). Square it (2116) and add it to both sides. Add '2116' to each side of the equation. 92x + 2116 + x2 = 5985 + 2116 Reorder the terms: 2116 + 92x + x2 = 5985 + 2116 Combine like terms: 5985 + 2116 = 8101 2116 + 92x + x2 = 8101 Factor a perfect square on the left side: (x + 46)(x + 46) = 8101 Calculate the square root of the right side: 90.005555384 Break this problem into two subproblems by setting (x + 46) equal to 90.005555384 and -90.005555384.Subproblem 1
x + 46 = 90.005555384 Simplifying x + 46 = 90.005555384 Reorder the terms: 46 + x = 90.005555384 Solving 46 + x = 90.005555384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + x = 90.005555384 + -46 Combine like terms: 46 + -46 = 0 0 + x = 90.005555384 + -46 x = 90.005555384 + -46 Combine like terms: 90.005555384 + -46 = 44.005555384 x = 44.005555384 Simplifying x = 44.005555384Subproblem 2
x + 46 = -90.005555384 Simplifying x + 46 = -90.005555384 Reorder the terms: 46 + x = -90.005555384 Solving 46 + x = -90.005555384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + x = -90.005555384 + -46 Combine like terms: 46 + -46 = 0 0 + x = -90.005555384 + -46 x = -90.005555384 + -46 Combine like terms: -90.005555384 + -46 = -136.005555384 x = -136.005555384 Simplifying x = -136.005555384Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.005555384, -136.005555384}
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