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Simplifying x2 + 10x + -184 = 0 Reorder the terms: -184 + 10x + x2 = 0 Solving -184 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '184' to each side of the equation. -184 + 10x + 184 + x2 = 0 + 184 Reorder the terms: -184 + 184 + 10x + x2 = 0 + 184 Combine like terms: -184 + 184 = 0 0 + 10x + x2 = 0 + 184 10x + x2 = 0 + 184 Combine like terms: 0 + 184 = 184 10x + x2 = 184 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 184 + 25 Reorder the terms: 25 + 10x + x2 = 184 + 25 Combine like terms: 184 + 25 = 209 25 + 10x + x2 = 209 Factor a perfect square on the left side: (x + 5)(x + 5) = 209 Calculate the square root of the right side: 14.456832295 Break this problem into two subproblems by setting (x + 5) equal to 14.456832295 and -14.456832295.Subproblem 1
x + 5 = 14.456832295 Simplifying x + 5 = 14.456832295 Reorder the terms: 5 + x = 14.456832295 Solving 5 + x = 14.456832295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 14.456832295 + -5 Combine like terms: 5 + -5 = 0 0 + x = 14.456832295 + -5 x = 14.456832295 + -5 Combine like terms: 14.456832295 + -5 = 9.456832295 x = 9.456832295 Simplifying x = 9.456832295Subproblem 2
x + 5 = -14.456832295 Simplifying x + 5 = -14.456832295 Reorder the terms: 5 + x = -14.456832295 Solving 5 + x = -14.456832295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -14.456832295 + -5 Combine like terms: 5 + -5 = 0 0 + x = -14.456832295 + -5 x = -14.456832295 + -5 Combine like terms: -14.456832295 + -5 = -19.456832295 x = -19.456832295 Simplifying x = -19.456832295Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.456832295, -19.456832295}
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