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Simplifying x2 + 25x + 35 = 0 Reorder the terms: 35 + 25x + x2 = 0 Solving 35 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 25x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + 25x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 25x + x2 = 0 + -35 25x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 25x + x2 = -35 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 = -35 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -35 + 156.25 Combine like terms: -35 + 156.25 = 121.25 156.25 + 25x + x2 = 121.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 121.25 Calculate the square root of the right side: 11.011357773 Break this problem into two subproblems by setting (x + 12.5) equal to 11.011357773 and -11.011357773.Subproblem 1
x + 12.5 = 11.011357773 Simplifying x + 12.5 = 11.011357773 Reorder the terms: 12.5 + x = 11.011357773 Solving 12.5 + x = 11.011357773 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 = 11.011357773 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 11.011357773 + -12.5 x = 11.011357773 + -12.5 Combine like terms: 11.011357773 + -12.5 = -1.488642227 x = -1.488642227 Simplifying x = -1.488642227Subproblem 2
x + 12.5 = -11.011357773 Simplifying x + 12.5 = -11.011357773 Reorder the terms: 12.5 + x = -11.011357773 Solving 12.5 + x = -11.011357773 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 = -11.011357773 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -11.011357773 + -12.5 x = -11.011357773 + -12.5 Combine like terms: -11.011357773 + -12.5 = -23.511357773 x = -23.511357773 Simplifying x = -23.511357773Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.488642227, -23.511357773}
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