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Simplifying x2 + 10x + -22001 = 0 Reorder the terms: -22001 + 10x + x2 = 0 Solving -22001 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '22001' to each side of the equation. -22001 + 10x + 22001 + x2 = 0 + 22001 Reorder the terms: -22001 + 22001 + 10x + x2 = 0 + 22001 Combine like terms: -22001 + 22001 = 0 0 + 10x + x2 = 0 + 22001 10x + x2 = 0 + 22001 Combine like terms: 0 + 22001 = 22001 10x + x2 = 22001 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 = 22001 + 25 Reorder the terms: 25 + 10x + x2 = 22001 + 25 Combine like terms: 22001 + 25 = 22026 25 + 10x + x2 = 22026 Factor a perfect square on the left side: (x + 5)(x + 5) = 22026 Calculate the square root of the right side: 148.411589844 Break this problem into two subproblems by setting (x + 5) equal to 148.411589844 and -148.411589844.Subproblem 1
x + 5 = 148.411589844 Simplifying x + 5 = 148.411589844 Reorder the terms: 5 + x = 148.411589844 Solving 5 + x = 148.411589844 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 = 148.411589844 + -5 Combine like terms: 5 + -5 = 0 0 + x = 148.411589844 + -5 x = 148.411589844 + -5 Combine like terms: 148.411589844 + -5 = 143.411589844 x = 143.411589844 Simplifying x = 143.411589844Subproblem 2
x + 5 = -148.411589844 Simplifying x + 5 = -148.411589844 Reorder the terms: 5 + x = -148.411589844 Solving 5 + x = -148.411589844 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 = -148.411589844 + -5 Combine like terms: 5 + -5 = 0 0 + x = -148.411589844 + -5 x = -148.411589844 + -5 Combine like terms: -148.411589844 + -5 = -153.411589844 x = -153.411589844 Simplifying x = -153.411589844Solution
The solution to the problem is based on the solutions from the subproblems. x = {143.411589844, -153.411589844}
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