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Simplifying 0 = x2 + -10x + -83 Reorder the terms: 0 = -83 + -10x + x2 Solving 0 = -83 + -10x + x2 Solving for variable 'x'. Combine like terms: 0 + 83 = 83 83 + 10x + -1x2 = -83 + -10x + x2 + 83 + 10x + -1x2 Reorder the terms: 83 + 10x + -1x2 = -83 + 83 + -10x + 10x + x2 + -1x2 Combine like terms: -83 + 83 = 0 83 + 10x + -1x2 = 0 + -10x + 10x + x2 + -1x2 83 + 10x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 83 + 10x + -1x2 = 0 + x2 + -1x2 83 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 83 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -83 + -10x + x2 = 0 Move the constant term to the right: Add '83' to each side of the equation. -83 + -10x + 83 + x2 = 0 + 83 Reorder the terms: -83 + 83 + -10x + x2 = 0 + 83 Combine like terms: -83 + 83 = 0 0 + -10x + x2 = 0 + 83 -10x + x2 = 0 + 83 Combine like terms: 0 + 83 = 83 -10x + x2 = 83 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 = 83 + 25 Reorder the terms: 25 + -10x + x2 = 83 + 25 Combine like terms: 83 + 25 = 108 25 + -10x + x2 = 108 Factor a perfect square on the left side: (x + -5)(x + -5) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + -5) equal to 10.392304845 and -10.392304845.Subproblem 1
x + -5 = 10.392304845 Simplifying x + -5 = 10.392304845 Reorder the terms: -5 + x = 10.392304845 Solving -5 + x = 10.392304845 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 = 10.392304845 + 5 Combine like terms: -5 + 5 = 0 0 + x = 10.392304845 + 5 x = 10.392304845 + 5 Combine like terms: 10.392304845 + 5 = 15.392304845 x = 15.392304845 Simplifying x = 15.392304845Subproblem 2
x + -5 = -10.392304845 Simplifying x + -5 = -10.392304845 Reorder the terms: -5 + x = -10.392304845 Solving -5 + x = -10.392304845 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 = -10.392304845 + 5 Combine like terms: -5 + 5 = 0 0 + x = -10.392304845 + 5 x = -10.392304845 + 5 Combine like terms: -10.392304845 + 5 = -5.392304845 x = -5.392304845 Simplifying x = -5.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.392304845, -5.392304845}
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