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Simplifying x2 + 7x + -128 = 0 Reorder the terms: -128 + 7x + x2 = 0 Solving -128 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '128' to each side of the equation. -128 + 7x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + 7x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 7x + x2 = 0 + 128 7x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 7x + x2 = 128 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 128 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 128 + 12.25 Combine like terms: 128 + 12.25 = 140.25 12.25 + 7x + x2 = 140.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (x + 3.5) equal to 11.842719282 and -11.842719282.Subproblem 1
x + 3.5 = 11.842719282 Simplifying x + 3.5 = 11.842719282 Reorder the terms: 3.5 + x = 11.842719282 Solving 3.5 + x = 11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 11.842719282 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 11.842719282 + -3.5 x = 11.842719282 + -3.5 Combine like terms: 11.842719282 + -3.5 = 8.342719282 x = 8.342719282 Simplifying x = 8.342719282Subproblem 2
x + 3.5 = -11.842719282 Simplifying x + 3.5 = -11.842719282 Reorder the terms: 3.5 + x = -11.842719282 Solving 3.5 + x = -11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -11.842719282 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -11.842719282 + -3.5 x = -11.842719282 + -3.5 Combine like terms: -11.842719282 + -3.5 = -15.342719282 x = -15.342719282 Simplifying x = -15.342719282Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.342719282, -15.342719282}
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