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Simplifying x2 + 25x + 11 = 0 Reorder the terms: 11 + 25x + x2 = 0 Solving 11 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 25x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 25x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 25x + x2 = 0 + -11 25x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 25x + x2 = -11 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 = -11 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -11 + 156.25 Combine like terms: -11 + 156.25 = 145.25 156.25 + 25x + x2 = 145.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 145.25 Calculate the square root of the right side: 12.051970793 Break this problem into two subproblems by setting (x + 12.5) equal to 12.051970793 and -12.051970793.Subproblem 1
x + 12.5 = 12.051970793 Simplifying x + 12.5 = 12.051970793 Reorder the terms: 12.5 + x = 12.051970793 Solving 12.5 + x = 12.051970793 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 = 12.051970793 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.051970793 + -12.5 x = 12.051970793 + -12.5 Combine like terms: 12.051970793 + -12.5 = -0.448029207 x = -0.448029207 Simplifying x = -0.448029207Subproblem 2
x + 12.5 = -12.051970793 Simplifying x + 12.5 = -12.051970793 Reorder the terms: 12.5 + x = -12.051970793 Solving 12.5 + x = -12.051970793 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 = -12.051970793 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.051970793 + -12.5 x = -12.051970793 + -12.5 Combine like terms: -12.051970793 + -12.5 = -24.551970793 x = -24.551970793 Simplifying x = -24.551970793Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.448029207, -24.551970793}
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