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Simplifying 2x2 + -14x + -129 = 0 Reorder the terms: -129 + -14x + 2x2 = 0 Solving -129 + -14x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -64.5 + -7x + x2 = 0 Move the constant term to the right: Add '64.5' to each side of the equation. -64.5 + -7x + 64.5 + x2 = 0 + 64.5 Reorder the terms: -64.5 + 64.5 + -7x + x2 = 0 + 64.5 Combine like terms: -64.5 + 64.5 = 0.0 0.0 + -7x + x2 = 0 + 64.5 -7x + x2 = 0 + 64.5 Combine like terms: 0 + 64.5 = 64.5 -7x + x2 = 64.5 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 = 64.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 64.5 + 12.25 Combine like terms: 64.5 + 12.25 = 76.75 12.25 + -7x + x2 = 76.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 76.75 Calculate the square root of the right side: 8.760707734 Break this problem into two subproblems by setting (x + -3.5) equal to 8.760707734 and -8.760707734.Subproblem 1
x + -3.5 = 8.760707734 Simplifying x + -3.5 = 8.760707734 Reorder the terms: -3.5 + x = 8.760707734 Solving -3.5 + x = 8.760707734 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 = 8.760707734 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 8.760707734 + 3.5 x = 8.760707734 + 3.5 Combine like terms: 8.760707734 + 3.5 = 12.260707734 x = 12.260707734 Simplifying x = 12.260707734Subproblem 2
x + -3.5 = -8.760707734 Simplifying x + -3.5 = -8.760707734 Reorder the terms: -3.5 + x = -8.760707734 Solving -3.5 + x = -8.760707734 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 = -8.760707734 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -8.760707734 + 3.5 x = -8.760707734 + 3.5 Combine like terms: -8.760707734 + 3.5 = -5.260707734 x = -5.260707734 Simplifying x = -5.260707734Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.260707734, -5.260707734}
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