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Simplifying x2 + -10x + -207 = 0 Reorder the terms: -207 + -10x + x2 = 0 Solving -207 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '207' to each side of the equation. -207 + -10x + 207 + x2 = 0 + 207 Reorder the terms: -207 + 207 + -10x + x2 = 0 + 207 Combine like terms: -207 + 207 = 0 0 + -10x + x2 = 0 + 207 -10x + x2 = 0 + 207 Combine like terms: 0 + 207 = 207 -10x + x2 = 207 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 = 207 + 25 Reorder the terms: 25 + -10x + x2 = 207 + 25 Combine like terms: 207 + 25 = 232 25 + -10x + x2 = 232 Factor a perfect square on the left side: (x + -5)(x + -5) = 232 Calculate the square root of the right side: 15.231546212 Break this problem into two subproblems by setting (x + -5) equal to 15.231546212 and -15.231546212.Subproblem 1
x + -5 = 15.231546212 Simplifying x + -5 = 15.231546212 Reorder the terms: -5 + x = 15.231546212 Solving -5 + x = 15.231546212 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 = 15.231546212 + 5 Combine like terms: -5 + 5 = 0 0 + x = 15.231546212 + 5 x = 15.231546212 + 5 Combine like terms: 15.231546212 + 5 = 20.231546212 x = 20.231546212 Simplifying x = 20.231546212Subproblem 2
x + -5 = -15.231546212 Simplifying x + -5 = -15.231546212 Reorder the terms: -5 + x = -15.231546212 Solving -5 + x = -15.231546212 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 = -15.231546212 + 5 Combine like terms: -5 + 5 = 0 0 + x = -15.231546212 + 5 x = -15.231546212 + 5 Combine like terms: -15.231546212 + 5 = -10.231546212 x = -10.231546212 Simplifying x = -10.231546212Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.231546212, -10.231546212}
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