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Simplifying x2 + -10x = 125 Reorder the terms: -10x + x2 = 125 Solving -10x + x2 = 125 Solving for variable 'x'. Reorder the terms: -125 + -10x + x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + -10x + x2 = 0 Begin completing the square. 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 = 17.247448714 x = 17.247448714 Simplifying x = 17.247448714Subproblem 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 = -7.247448714 x = -7.247448714 Simplifying x = -7.247448714Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.247448714, -7.247448714}
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