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Simplifying x2 + 10x + -121 = 0 Reorder the terms: -121 + 10x + x2 = 0 Solving -121 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '121' to each side of the equation. -121 + 10x + 121 + x2 = 0 + 121 Reorder the terms: -121 + 121 + 10x + x2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + 10x + x2 = 0 + 121 10x + x2 = 0 + 121 Combine like terms: 0 + 121 = 121 10x + x2 = 121 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 = 121 + 25 Reorder the terms: 25 + 10x + x2 = 121 + 25 Combine like terms: 121 + 25 = 146 25 + 10x + x2 = 146 Factor a perfect square on the left side: (x + 5)(x + 5) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (x + 5) equal to 12.083045974 and -12.083045974.Subproblem 1
x + 5 = 12.083045974 Simplifying x + 5 = 12.083045974 Reorder the terms: 5 + x = 12.083045974 Solving 5 + x = 12.083045974 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 = 12.083045974 + -5 Combine like terms: 5 + -5 = 0 0 + x = 12.083045974 + -5 x = 12.083045974 + -5 Combine like terms: 12.083045974 + -5 = 7.083045974 x = 7.083045974 Simplifying x = 7.083045974Subproblem 2
x + 5 = -12.083045974 Simplifying x + 5 = -12.083045974 Reorder the terms: 5 + x = -12.083045974 Solving 5 + x = -12.083045974 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 = -12.083045974 + -5 Combine like terms: 5 + -5 = 0 0 + x = -12.083045974 + -5 x = -12.083045974 + -5 Combine like terms: -12.083045974 + -5 = -17.083045974 x = -17.083045974 Simplifying x = -17.083045974Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.083045974, -17.083045974}
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