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Simplifying -1x2 + -7x + 196 = 0 Reorder the terms: 196 + -7x + -1x2 = 0 Solving 196 + -7x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -196 + 7x + x2 = 0 Move the constant term to the right: Add '196' to each side of the equation. -196 + 7x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + 7x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 7x + x2 = 0 + 196 7x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 7x + x2 = 196 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 = 196 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 196 + 12.25 Combine like terms: 196 + 12.25 = 208.25 12.25 + 7x + x2 = 208.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 208.25 Calculate the square root of the right side: 14.43086969 Break this problem into two subproblems by setting (x + 3.5) equal to 14.43086969 and -14.43086969.Subproblem 1
x + 3.5 = 14.43086969 Simplifying x + 3.5 = 14.43086969 Reorder the terms: 3.5 + x = 14.43086969 Solving 3.5 + x = 14.43086969 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 = 14.43086969 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 14.43086969 + -3.5 x = 14.43086969 + -3.5 Combine like terms: 14.43086969 + -3.5 = 10.93086969 x = 10.93086969 Simplifying x = 10.93086969Subproblem 2
x + 3.5 = -14.43086969 Simplifying x + 3.5 = -14.43086969 Reorder the terms: 3.5 + x = -14.43086969 Solving 3.5 + x = -14.43086969 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 = -14.43086969 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -14.43086969 + -3.5 x = -14.43086969 + -3.5 Combine like terms: -14.43086969 + -3.5 = -17.93086969 x = -17.93086969 Simplifying x = -17.93086969Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.93086969, -17.93086969}
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