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Simplifying 0 = x2 + 6x + -128 Reorder the terms: 0 = -128 + 6x + x2 Solving 0 = -128 + 6x + x2 Solving for variable 'x'. Combine like terms: 0 + 128 = 128 128 + -6x + -1x2 = -128 + 6x + x2 + 128 + -6x + -1x2 Reorder the terms: 128 + -6x + -1x2 = -128 + 128 + 6x + -6x + x2 + -1x2 Combine like terms: -128 + 128 = 0 128 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 128 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 128 + -6x + -1x2 = 0 + x2 + -1x2 128 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 128 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -128 + 6x + x2 = 0 Move the constant term to the right: Add '128' to each side of the equation. -128 + 6x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + 6x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 6x + x2 = 0 + 128 6x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 6x + x2 = 128 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 128 + 9 Reorder the terms: 9 + 6x + x2 = 128 + 9 Combine like terms: 128 + 9 = 137 9 + 6x + x2 = 137 Factor a perfect square on the left side: (x + 3)(x + 3) = 137 Calculate the square root of the right side: 11.704699911 Break this problem into two subproblems by setting (x + 3) equal to 11.704699911 and -11.704699911.Subproblem 1
x + 3 = 11.704699911 Simplifying x + 3 = 11.704699911 Reorder the terms: 3 + x = 11.704699911 Solving 3 + x = 11.704699911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 11.704699911 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.704699911 + -3 x = 11.704699911 + -3 Combine like terms: 11.704699911 + -3 = 8.704699911 x = 8.704699911 Simplifying x = 8.704699911Subproblem 2
x + 3 = -11.704699911 Simplifying x + 3 = -11.704699911 Reorder the terms: 3 + x = -11.704699911 Solving 3 + x = -11.704699911 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -11.704699911 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.704699911 + -3 x = -11.704699911 + -3 Combine like terms: -11.704699911 + -3 = -14.704699911 x = -14.704699911 Simplifying x = -14.704699911Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.704699911, -14.704699911}
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