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Simplifying x2 + 25x + 0.04 = 0 Reorder the terms: 0.04 + 25x + x2 = 0 Solving 0.04 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + 25x + -0.04 + x2 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + 25x + x2 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + 25x + x2 = 0 + -0.04 25x + x2 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 25x + x2 = -0.04 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 = -0.04 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -0.04 + 156.25 Combine like terms: -0.04 + 156.25 = 156.21 156.25 + 25x + x2 = 156.21 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 156.21 Calculate the square root of the right side: 12.498399898 Break this problem into two subproblems by setting (x + 12.5) equal to 12.498399898 and -12.498399898.Subproblem 1
x + 12.5 = 12.498399898 Simplifying x + 12.5 = 12.498399898 Reorder the terms: 12.5 + x = 12.498399898 Solving 12.5 + x = 12.498399898 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 = 12.498399898 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.498399898 + -12.5 x = 12.498399898 + -12.5 Combine like terms: 12.498399898 + -12.5 = -0.001600102 x = -0.001600102 Simplifying x = -0.001600102Subproblem 2
x + 12.5 = -12.498399898 Simplifying x + 12.5 = -12.498399898 Reorder the terms: 12.5 + x = -12.498399898 Solving 12.5 + x = -12.498399898 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 = -12.498399898 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.498399898 + -12.5 x = -12.498399898 + -12.5 Combine like terms: -12.498399898 + -12.5 = -24.998399898 x = -24.998399898 Simplifying x = -24.998399898Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.001600102, -24.998399898}
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