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Simplifying x2 + 25x + -18 = 0 Reorder the terms: -18 + 25x + x2 = 0 Solving -18 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 25x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 25x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 25x + x2 = 0 + 18 25x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 25x + x2 = 18 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 = 18 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 18 + 156.25 Combine like terms: 18 + 156.25 = 174.25 156.25 + 25x + x2 = 174.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 174.25 Calculate the square root of the right side: 13.200378782 Break this problem into two subproblems by setting (x + 12.5) equal to 13.200378782 and -13.200378782.Subproblem 1
x + 12.5 = 13.200378782 Simplifying x + 12.5 = 13.200378782 Reorder the terms: 12.5 + x = 13.200378782 Solving 12.5 + x = 13.200378782 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 = 13.200378782 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 13.200378782 + -12.5 x = 13.200378782 + -12.5 Combine like terms: 13.200378782 + -12.5 = 0.700378782 x = 0.700378782 Simplifying x = 0.700378782Subproblem 2
x + 12.5 = -13.200378782 Simplifying x + 12.5 = -13.200378782 Reorder the terms: 12.5 + x = -13.200378782 Solving 12.5 + x = -13.200378782 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 = -13.200378782 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -13.200378782 + -12.5 x = -13.200378782 + -12.5 Combine like terms: -13.200378782 + -12.5 = -25.700378782 x = -25.700378782 Simplifying x = -25.700378782Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.700378782, -25.700378782}
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