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Simplifying x2 + 95x + 14 = 0 Reorder the terms: 14 + 95x + x2 = 0 Solving 14 + 95x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 95x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 95x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 95x + x2 = 0 + -14 95x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 95x + x2 = -14 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 = -14 + 2256.25 Reorder the terms: 2256.25 + 95x + x2 = -14 + 2256.25 Combine like terms: -14 + 2256.25 = 2242.25 2256.25 + 95x + x2 = 2242.25 Factor a perfect square on the left side: (x + 47.5)(x + 47.5) = 2242.25 Calculate the square root of the right side: 47.352402262 Break this problem into two subproblems by setting (x + 47.5) equal to 47.352402262 and -47.352402262.Subproblem 1
x + 47.5 = 47.352402262 Simplifying x + 47.5 = 47.352402262 Reorder the terms: 47.5 + x = 47.352402262 Solving 47.5 + x = 47.352402262 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 = 47.352402262 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + x = 47.352402262 + -47.5 x = 47.352402262 + -47.5 Combine like terms: 47.352402262 + -47.5 = -0.147597738 x = -0.147597738 Simplifying x = -0.147597738Subproblem 2
x + 47.5 = -47.352402262 Simplifying x + 47.5 = -47.352402262 Reorder the terms: 47.5 + x = -47.352402262 Solving 47.5 + x = -47.352402262 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 = -47.352402262 + -47.5 Combine like terms: 47.5 + -47.5 = 0.0 0.0 + x = -47.352402262 + -47.5 x = -47.352402262 + -47.5 Combine like terms: -47.352402262 + -47.5 = -94.852402262 x = -94.852402262 Simplifying x = -94.852402262Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.147597738, -94.852402262}
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