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Simplifying x2 + -10x + -133 = -6 Reorder the terms: -133 + -10x + x2 = -6 Solving -133 + -10x + x2 = -6 Solving for variable 'x'. Reorder the terms: -133 + 6 + -10x + x2 = -6 + 6 Combine like terms: -133 + 6 = -127 -127 + -10x + x2 = -6 + 6 Combine like terms: -6 + 6 = 0 -127 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '127' to each side of the equation. -127 + -10x + 127 + x2 = 0 + 127 Reorder the terms: -127 + 127 + -10x + x2 = 0 + 127 Combine like terms: -127 + 127 = 0 0 + -10x + x2 = 0 + 127 -10x + x2 = 0 + 127 Combine like terms: 0 + 127 = 127 -10x + x2 = 127 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 = 127 + 25 Reorder the terms: 25 + -10x + x2 = 127 + 25 Combine like terms: 127 + 25 = 152 25 + -10x + x2 = 152 Factor a perfect square on the left side: (x + -5)(x + -5) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (x + -5) equal to 12.328828006 and -12.328828006.Subproblem 1
x + -5 = 12.328828006 Simplifying x + -5 = 12.328828006 Reorder the terms: -5 + x = 12.328828006 Solving -5 + x = 12.328828006 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 = 12.328828006 + 5 Combine like terms: -5 + 5 = 0 0 + x = 12.328828006 + 5 x = 12.328828006 + 5 Combine like terms: 12.328828006 + 5 = 17.328828006 x = 17.328828006 Simplifying x = 17.328828006Subproblem 2
x + -5 = -12.328828006 Simplifying x + -5 = -12.328828006 Reorder the terms: -5 + x = -12.328828006 Solving -5 + x = -12.328828006 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 = -12.328828006 + 5 Combine like terms: -5 + 5 = 0 0 + x = -12.328828006 + 5 x = -12.328828006 + 5 Combine like terms: -12.328828006 + 5 = -7.328828006 x = -7.328828006 Simplifying x = -7.328828006Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.328828006, -7.328828006}
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