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Simplifying x2 + 95x + 96 = 0 Reorder the terms: 96 + 95x + x2 = 0 Solving 96 + 95x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-96' to each side of the equation. 96 + 95x + -96 + x2 = 0 + -96 Reorder the terms: 96 + -96 + 95x + x2 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + 95x + x2 = 0 + -96 95x + x2 = 0 + -96 Combine like terms: 0 + -96 = -96 95x + x2 = -96 The x term is 95x. Take half its coefficient (47.5). Square it (2256.25) and add it to both sides. Add '2256.25' to each side of the equation. 95x + 2256.25 + x2 = -96 + 2256.25 Reorder the terms: 2256.25 + 95x + x2 = -96 + 2256.25 Combine like terms: -96 + 2256.25 = 2160.25 2256.25 + 95x + x2 = 2160.25 Factor a perfect square on the left side: (x + 47.5)(x + 47.5) = 2160.25 Calculate the square root of the right side: 46.478489648 Break this problem into two subproblems by setting (x + 47.5) equal to 46.478489648 and -46.478489648.Subproblem 1
x + 47.5 = 46.478489648 Simplifying x + 47.5 = 46.478489648 Reorder the terms: 47.5 + x = 46.478489648 Solving 47.5 + x = 46.478489648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + x = 46.478489648 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + x = 46.478489648 + -47.5 x = 46.478489648 + -47.5 Combine like terms: 46.478489648 + -47.5 = -1.021510352 x = -1.021510352 Simplifying x = -1.021510352Subproblem 2
x + 47.5 = -46.478489648 Simplifying x + 47.5 = -46.478489648 Reorder the terms: 47.5 + x = -46.478489648 Solving 47.5 + x = -46.478489648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-47.5' to each side of the equation. 47.5 + -47.5 + x = -46.478489648 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + x = -46.478489648 + -47.5 x = -46.478489648 + -47.5 Combine like terms: -46.478489648 + -47.5 = -93.978489648 x = -93.978489648 Simplifying x = -93.978489648Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.021510352, -93.978489648}
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