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Simplifying 2x2 + 14x + -169 = 0 Reorder the terms: -169 + 14x + 2x2 = 0 Solving -169 + 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'. -84.5 + 7x + x2 = 0 Move the constant term to the right: Add '84.5' to each side of the equation. -84.5 + 7x + 84.5 + x2 = 0 + 84.5 Reorder the terms: -84.5 + 84.5 + 7x + x2 = 0 + 84.5 Combine like terms: -84.5 + 84.5 = 0.0 0.0 + 7x + x2 = 0 + 84.5 7x + x2 = 0 + 84.5 Combine like terms: 0 + 84.5 = 84.5 7x + x2 = 84.5 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 = 84.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 84.5 + 12.25 Combine like terms: 84.5 + 12.25 = 96.75 12.25 + 7x + x2 = 96.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 96.75 Calculate the square root of the right side: 9.836157786 Break this problem into two subproblems by setting (x + 3.5) equal to 9.836157786 and -9.836157786.Subproblem 1
x + 3.5 = 9.836157786 Simplifying x + 3.5 = 9.836157786 Reorder the terms: 3.5 + x = 9.836157786 Solving 3.5 + x = 9.836157786 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 = 9.836157786 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9.836157786 + -3.5 x = 9.836157786 + -3.5 Combine like terms: 9.836157786 + -3.5 = 6.336157786 x = 6.336157786 Simplifying x = 6.336157786Subproblem 2
x + 3.5 = -9.836157786 Simplifying x + 3.5 = -9.836157786 Reorder the terms: 3.5 + x = -9.836157786 Solving 3.5 + x = -9.836157786 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 = -9.836157786 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9.836157786 + -3.5 x = -9.836157786 + -3.5 Combine like terms: -9.836157786 + -3.5 = -13.336157786 x = -13.336157786 Simplifying x = -13.336157786Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.336157786, -13.336157786}
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