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Simplifying x2 + 10x + 25 = 1000 Reorder the terms: 25 + 10x + x2 = 1000 Solving 25 + 10x + x2 = 1000 Solving for variable 'x'. Reorder the terms: 25 + -1000 + 10x + x2 = 1000 + -1000 Combine like terms: 25 + -1000 = -975 -975 + 10x + x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -975 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '975' to each side of the equation. -975 + 10x + 975 + x2 = 0 + 975 Reorder the terms: -975 + 975 + 10x + x2 = 0 + 975 Combine like terms: -975 + 975 = 0 0 + 10x + x2 = 0 + 975 10x + x2 = 0 + 975 Combine like terms: 0 + 975 = 975 10x + x2 = 975 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 = 975 + 25 Reorder the terms: 25 + 10x + x2 = 975 + 25 Combine like terms: 975 + 25 = 1000 25 + 10x + x2 = 1000 Factor a perfect square on the left side: (x + 5)(x + 5) = 1000 Calculate the square root of the right side: 31.622776602 Break this problem into two subproblems by setting (x + 5) equal to 31.622776602 and -31.622776602.Subproblem 1
x + 5 = 31.622776602 Simplifying x + 5 = 31.622776602 Reorder the terms: 5 + x = 31.622776602 Solving 5 + x = 31.622776602 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 = 31.622776602 + -5 Combine like terms: 5 + -5 = 0 0 + x = 31.622776602 + -5 x = 31.622776602 + -5 Combine like terms: 31.622776602 + -5 = 26.622776602 x = 26.622776602 Simplifying x = 26.622776602Subproblem 2
x + 5 = -31.622776602 Simplifying x + 5 = -31.622776602 Reorder the terms: 5 + x = -31.622776602 Solving 5 + x = -31.622776602 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 = -31.622776602 + -5 Combine like terms: 5 + -5 = 0 0 + x = -31.622776602 + -5 x = -31.622776602 + -5 Combine like terms: -31.622776602 + -5 = -36.622776602 x = -36.622776602 Simplifying x = -36.622776602Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.622776602, -36.622776602}
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