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Simplifying 52 + -1x2 + 10x = 10 Reorder the terms: 52 + 10x + -1x2 = 10 Solving 52 + 10x + -1x2 = 10 Solving for variable 'x'. Reorder the terms: 52 + -10 + 10x + -1x2 = 10 + -10 Combine like terms: 52 + -10 = 42 42 + 10x + -1x2 = 10 + -10 Combine like terms: 10 + -10 = 0 42 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -42 + -10x + x2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + -10x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -10x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -10x + x2 = 0 + 42 -10x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -10x + x2 = 42 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 = 42 + 25 Reorder the terms: 25 + -10x + x2 = 42 + 25 Combine like terms: 42 + 25 = 67 25 + -10x + x2 = 67 Factor a perfect square on the left side: (x + -5)(x + -5) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + -5) equal to 8.185352772 and -8.185352772.Subproblem 1
x + -5 = 8.185352772 Simplifying x + -5 = 8.185352772 Reorder the terms: -5 + x = 8.185352772 Solving -5 + x = 8.185352772 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 = 8.185352772 + 5 Combine like terms: -5 + 5 = 0 0 + x = 8.185352772 + 5 x = 8.185352772 + 5 Combine like terms: 8.185352772 + 5 = 13.185352772 x = 13.185352772 Simplifying x = 13.185352772Subproblem 2
x + -5 = -8.185352772 Simplifying x + -5 = -8.185352772 Reorder the terms: -5 + x = -8.185352772 Solving -5 + x = -8.185352772 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 = -8.185352772 + 5 Combine like terms: -5 + 5 = 0 0 + x = -8.185352772 + 5 x = -8.185352772 + 5 Combine like terms: -8.185352772 + 5 = -3.185352772 x = -3.185352772 Simplifying x = -3.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.185352772, -3.185352772}
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