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Simplifying x2 + 14x + -196 = 0 Reorder the terms: -196 + 14x + x2 = 0 Solving -196 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + 14x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + 14x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 14x + x2 = 0 + 196 14x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 14x + x2 = 196 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 196 + 49 Reorder the terms: 49 + 14x + x2 = 196 + 49 Combine like terms: 196 + 49 = 245 49 + 14x + x2 = 245 Factor a perfect square on the left side: (x + 7)(x + 7) = 245 Calculate the square root of the right side: 15.652475842 Break this problem into two subproblems by setting (x + 7) equal to 15.652475842 and -15.652475842.Subproblem 1
x + 7 = 15.652475842 Simplifying x + 7 = 15.652475842 Reorder the terms: 7 + x = 15.652475842 Solving 7 + x = 15.652475842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 15.652475842 + -7 Combine like terms: 7 + -7 = 0 0 + x = 15.652475842 + -7 x = 15.652475842 + -7 Combine like terms: 15.652475842 + -7 = 8.652475842 x = 8.652475842 Simplifying x = 8.652475842Subproblem 2
x + 7 = -15.652475842 Simplifying x + 7 = -15.652475842 Reorder the terms: 7 + x = -15.652475842 Solving 7 + x = -15.652475842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -15.652475842 + -7 Combine like terms: 7 + -7 = 0 0 + x = -15.652475842 + -7 x = -15.652475842 + -7 Combine like terms: -15.652475842 + -7 = -22.652475842 x = -22.652475842 Simplifying x = -22.652475842Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.652475842, -22.652475842}
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