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Simplifying x2 + 25x + 12 = 0 Reorder the terms: 12 + 25x + x2 = 0 Solving 12 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 25x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 25x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 25x + x2 = 0 + -12 25x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 25x + x2 = -12 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 = -12 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -12 + 156.25 Combine like terms: -12 + 156.25 = 144.25 156.25 + 25x + x2 = 144.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (x + 12.5) equal to 12.010412149 and -12.010412149.Subproblem 1
x + 12.5 = 12.010412149 Simplifying x + 12.5 = 12.010412149 Reorder the terms: 12.5 + x = 12.010412149 Solving 12.5 + x = 12.010412149 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 = 12.010412149 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.010412149 + -12.5 x = 12.010412149 + -12.5 Combine like terms: 12.010412149 + -12.5 = -0.489587851 x = -0.489587851 Simplifying x = -0.489587851Subproblem 2
x + 12.5 = -12.010412149 Simplifying x + 12.5 = -12.010412149 Reorder the terms: 12.5 + x = -12.010412149 Solving 12.5 + x = -12.010412149 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 = -12.010412149 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.010412149 + -12.5 x = -12.010412149 + -12.5 Combine like terms: -12.010412149 + -12.5 = -24.510412149 x = -24.510412149 Simplifying x = -24.510412149Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.489587851, -24.510412149}
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