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Simplifying x2 + -196 = x Reorder the terms: -196 + x2 = x Solving -196 + x2 = x Solving for variable 'x'. Reorder the terms: -196 + -1x + x2 = x + -1x Combine like terms: x + -1x = 0 -196 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + -1x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + -1x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + -1x + x2 = 0 + 196 -1x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 -1x + x2 = 196 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 196 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 196 + 0.25 Combine like terms: 196 + 0.25 = 196.25 0.25 + -1x + x2 = 196.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 196.25 Calculate the square root of the right side: 14.008925726 Break this problem into two subproblems by setting (x + -0.5) equal to 14.008925726 and -14.008925726.Subproblem 1
x + -0.5 = 14.008925726 Simplifying x + -0.5 = 14.008925726 Reorder the terms: -0.5 + x = 14.008925726 Solving -0.5 + x = 14.008925726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 14.008925726 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 14.008925726 + 0.5 x = 14.008925726 + 0.5 Combine like terms: 14.008925726 + 0.5 = 14.508925726 x = 14.508925726 Simplifying x = 14.508925726Subproblem 2
x + -0.5 = -14.008925726 Simplifying x + -0.5 = -14.008925726 Reorder the terms: -0.5 + x = -14.008925726 Solving -0.5 + x = -14.008925726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -14.008925726 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -14.008925726 + 0.5 x = -14.008925726 + 0.5 Combine like terms: -14.008925726 + 0.5 = -13.508925726 x = -13.508925726 Simplifying x = -13.508925726Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.508925726, -13.508925726}
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