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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 = 7.369316877 x = 7.369316877 Simplifying x = 7.369316877Subproblem 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 = -17.369316877 x = -17.369316877 Simplifying x = -17.369316877Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.369316877, -17.369316877}
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