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Simplifying x2 + 10x + 21 = 1089 Reorder the terms: 21 + 10x + x2 = 1089 Solving 21 + 10x + x2 = 1089 Solving for variable 'x'. Reorder the terms: 21 + -1089 + 10x + x2 = 1089 + -1089 Combine like terms: 21 + -1089 = -1068 -1068 + 10x + x2 = 1089 + -1089 Combine like terms: 1089 + -1089 = 0 -1068 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1068' to each side of the equation. -1068 + 10x + 1068 + x2 = 0 + 1068 Reorder the terms: -1068 + 1068 + 10x + x2 = 0 + 1068 Combine like terms: -1068 + 1068 = 0 0 + 10x + x2 = 0 + 1068 10x + x2 = 0 + 1068 Combine like terms: 0 + 1068 = 1068 10x + x2 = 1068 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 = 1068 + 25 Reorder the terms: 25 + 10x + x2 = 1068 + 25 Combine like terms: 1068 + 25 = 1093 25 + 10x + x2 = 1093 Factor a perfect square on the left side: (x + 5)(x + 5) = 1093 Calculate the square root of the right side: 33.06055051 Break this problem into two subproblems by setting (x + 5) equal to 33.06055051 and -33.06055051.Subproblem 1
x + 5 = 33.06055051 Simplifying x + 5 = 33.06055051 Reorder the terms: 5 + x = 33.06055051 Solving 5 + x = 33.06055051 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 = 33.06055051 + -5 Combine like terms: 5 + -5 = 0 0 + x = 33.06055051 + -5 x = 33.06055051 + -5 Combine like terms: 33.06055051 + -5 = 28.06055051 x = 28.06055051 Simplifying x = 28.06055051Subproblem 2
x + 5 = -33.06055051 Simplifying x + 5 = -33.06055051 Reorder the terms: 5 + x = -33.06055051 Solving 5 + x = -33.06055051 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 = -33.06055051 + -5 Combine like terms: 5 + -5 = 0 0 + x = -33.06055051 + -5 x = -33.06055051 + -5 Combine like terms: -33.06055051 + -5 = -38.06055051 x = -38.06055051 Simplifying x = -38.06055051Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.06055051, -38.06055051}
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