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Simplifying x2 + 10x + -89 = 0 Reorder the terms: -89 + 10x + x2 = 0 Solving -89 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + 10x + 89 + x2 = 0 + 89 Reorder the terms: -89 + 89 + 10x + x2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 10x + x2 = 0 + 89 10x + x2 = 0 + 89 Combine like terms: 0 + 89 = 89 10x + x2 = 89 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 = 89 + 25 Reorder the terms: 25 + 10x + x2 = 89 + 25 Combine like terms: 89 + 25 = 114 25 + 10x + x2 = 114 Factor a perfect square on the left side: (x + 5)(x + 5) = 114 Calculate the square root of the right side: 10.677078252 Break this problem into two subproblems by setting (x + 5) equal to 10.677078252 and -10.677078252.Subproblem 1
x + 5 = 10.677078252 Simplifying x + 5 = 10.677078252 Reorder the terms: 5 + x = 10.677078252 Solving 5 + x = 10.677078252 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 = 10.677078252 + -5 Combine like terms: 5 + -5 = 0 0 + x = 10.677078252 + -5 x = 10.677078252 + -5 Combine like terms: 10.677078252 + -5 = 5.677078252 x = 5.677078252 Simplifying x = 5.677078252Subproblem 2
x + 5 = -10.677078252 Simplifying x + 5 = -10.677078252 Reorder the terms: 5 + x = -10.677078252 Solving 5 + x = -10.677078252 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 = -10.677078252 + -5 Combine like terms: 5 + -5 = 0 0 + x = -10.677078252 + -5 x = -10.677078252 + -5 Combine like terms: -10.677078252 + -5 = -15.677078252 x = -15.677078252 Simplifying x = -15.677078252Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.677078252, -15.677078252}
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