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Simplifying 125 + -1x2 + -10x = 0 Reorder the terms: 125 + -10x + -1x2 = 0 Solving 125 + -10x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -125 + 10x + x2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + 10x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + 10x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 10x + x2 = 0 + 125 10x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 10x + x2 = 125 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 = 125 + 25 Reorder the terms: 25 + 10x + x2 = 125 + 25 Combine like terms: 125 + 25 = 150 25 + 10x + x2 = 150 Factor a perfect square on the left side: (x + 5)(x + 5) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (x + 5) equal to 12.247448714 and -12.247448714.Subproblem 1
x + 5 = 12.247448714 Simplifying x + 5 = 12.247448714 Reorder the terms: 5 + x = 12.247448714 Solving 5 + x = 12.247448714 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 = 12.247448714 + -5 Combine like terms: 5 + -5 = 0 0 + x = 12.247448714 + -5 x = 12.247448714 + -5 Combine like terms: 12.247448714 + -5 = 7.247448714 x = 7.247448714 Simplifying x = 7.247448714Subproblem 2
x + 5 = -12.247448714 Simplifying x + 5 = -12.247448714 Reorder the terms: 5 + x = -12.247448714 Solving 5 + x = -12.247448714 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 = -12.247448714 + -5 Combine like terms: 5 + -5 = 0 0 + x = -12.247448714 + -5 x = -12.247448714 + -5 Combine like terms: -12.247448714 + -5 = -17.247448714 x = -17.247448714 Simplifying x = -17.247448714Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.247448714, -17.247448714}
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