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Simplifying x2 + 10x + -94 = 0 Reorder the terms: -94 + 10x + x2 = 0 Solving -94 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '94' to each side of the equation. -94 + 10x + 94 + x2 = 0 + 94 Reorder the terms: -94 + 94 + 10x + x2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + 10x + x2 = 0 + 94 10x + x2 = 0 + 94 Combine like terms: 0 + 94 = 94 10x + x2 = 94 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 = 94 + 25 Reorder the terms: 25 + 10x + x2 = 94 + 25 Combine like terms: 94 + 25 = 119 25 + 10x + x2 = 119 Factor a perfect square on the left side: (x + 5)(x + 5) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (x + 5) equal to 10.908712115 and -10.908712115.Subproblem 1
x + 5 = 10.908712115 Simplifying x + 5 = 10.908712115 Reorder the terms: 5 + x = 10.908712115 Solving 5 + x = 10.908712115 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 = 10.908712115 + -5 Combine like terms: 5 + -5 = 0 0 + x = 10.908712115 + -5 x = 10.908712115 + -5 Combine like terms: 10.908712115 + -5 = 5.908712115 x = 5.908712115 Simplifying x = 5.908712115Subproblem 2
x + 5 = -10.908712115 Simplifying x + 5 = -10.908712115 Reorder the terms: 5 + x = -10.908712115 Solving 5 + x = -10.908712115 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 = -10.908712115 + -5 Combine like terms: 5 + -5 = 0 0 + x = -10.908712115 + -5 x = -10.908712115 + -5 Combine like terms: -10.908712115 + -5 = -15.908712115 x = -15.908712115 Simplifying x = -15.908712115Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.908712115, -15.908712115}
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