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Simplifying x2 + -10x + -134 = 0 Reorder the terms: -134 + -10x + x2 = 0 Solving -134 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '134' to each side of the equation. -134 + -10x + 134 + x2 = 0 + 134 Reorder the terms: -134 + 134 + -10x + x2 = 0 + 134 Combine like terms: -134 + 134 = 0 0 + -10x + x2 = 0 + 134 -10x + x2 = 0 + 134 Combine like terms: 0 + 134 = 134 -10x + x2 = 134 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 = 134 + 25 Reorder the terms: 25 + -10x + x2 = 134 + 25 Combine like terms: 134 + 25 = 159 25 + -10x + x2 = 159 Factor a perfect square on the left side: (x + -5)(x + -5) = 159 Calculate the square root of the right side: 12.609520213 Break this problem into two subproblems by setting (x + -5) equal to 12.609520213 and -12.609520213.Subproblem 1
x + -5 = 12.609520213 Simplifying x + -5 = 12.609520213 Reorder the terms: -5 + x = 12.609520213 Solving -5 + x = 12.609520213 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 = 12.609520213 + 5 Combine like terms: -5 + 5 = 0 0 + x = 12.609520213 + 5 x = 12.609520213 + 5 Combine like terms: 12.609520213 + 5 = 17.609520213 x = 17.609520213 Simplifying x = 17.609520213Subproblem 2
x + -5 = -12.609520213 Simplifying x + -5 = -12.609520213 Reorder the terms: -5 + x = -12.609520213 Solving -5 + x = -12.609520213 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 = -12.609520213 + 5 Combine like terms: -5 + 5 = 0 0 + x = -12.609520213 + 5 x = -12.609520213 + 5 Combine like terms: -12.609520213 + 5 = -7.609520213 x = -7.609520213 Simplifying x = -7.609520213Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.609520213, -7.609520213}
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