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Simplifying 4 + 125x + 5x2 = 0 Solving 4 + 125x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 25x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 25x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 25x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 25x + x2 = 0 + -0.8 25x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 25x + x2 = -0.8 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = -0.8 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -0.8 + 156.25 Combine like terms: -0.8 + 156.25 = 155.45 156.25 + 25x + x2 = 155.45 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 155.45 Calculate the square root of the right side: 12.467958935 Break this problem into two subproblems by setting (x + 12.5) equal to 12.467958935 and -12.467958935.Subproblem 1
x + 12.5 = 12.467958935 Simplifying x + 12.5 = 12.467958935 Reorder the terms: 12.5 + x = 12.467958935 Solving 12.5 + x = 12.467958935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 12.467958935 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.467958935 + -12.5 x = 12.467958935 + -12.5 Combine like terms: 12.467958935 + -12.5 = -0.032041065 x = -0.032041065 Simplifying x = -0.032041065Subproblem 2
x + 12.5 = -12.467958935 Simplifying x + 12.5 = -12.467958935 Reorder the terms: 12.5 + x = -12.467958935 Solving 12.5 + x = -12.467958935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -12.467958935 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.467958935 + -12.5 x = -12.467958935 + -12.5 Combine like terms: -12.467958935 + -12.5 = -24.967958935 x = -24.967958935 Simplifying x = -24.967958935Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.032041065, -24.967958935}
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