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Simplifying 0 = x2 + -10x + -128 Reorder the terms: 0 = -128 + -10x + x2 Solving 0 = -128 + -10x + x2 Solving for variable 'x'. Combine like terms: 0 + 128 = 128 128 + 10x + -1x2 = -128 + -10x + x2 + 128 + 10x + -1x2 Reorder the terms: 128 + 10x + -1x2 = -128 + 128 + -10x + 10x + x2 + -1x2 Combine like terms: -128 + 128 = 0 128 + 10x + -1x2 = 0 + -10x + 10x + x2 + -1x2 128 + 10x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 128 + 10x + -1x2 = 0 + x2 + -1x2 128 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 128 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -128 + -10x + x2 = 0 Move the constant term to the right: Add '128' to each side of the equation. -128 + -10x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + -10x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + -10x + x2 = 0 + 128 -10x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 -10x + x2 = 128 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 = 128 + 25 Reorder the terms: 25 + -10x + x2 = 128 + 25 Combine like terms: 128 + 25 = 153 25 + -10x + x2 = 153 Factor a perfect square on the left side: (x + -5)(x + -5) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (x + -5) equal to 12.369316877 and -12.369316877.Subproblem 1
x + -5 = 12.369316877 Simplifying x + -5 = 12.369316877 Reorder the terms: -5 + x = 12.369316877 Solving -5 + x = 12.369316877 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 = 12.369316877 + 5 Combine like terms: -5 + 5 = 0 0 + x = 12.369316877 + 5 x = 12.369316877 + 5 Combine like terms: 12.369316877 + 5 = 17.369316877 x = 17.369316877 Simplifying x = 17.369316877Subproblem 2
x + -5 = -12.369316877 Simplifying x + -5 = -12.369316877 Reorder the terms: -5 + x = -12.369316877 Solving -5 + x = -12.369316877 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 = -12.369316877 + 5 Combine like terms: -5 + 5 = 0 0 + x = -12.369316877 + 5 x = -12.369316877 + 5 Combine like terms: -12.369316877 + 5 = -7.369316877 x = -7.369316877 Simplifying x = -7.369316877Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.369316877, -7.369316877}
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