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Simplifying x2 + -25x + -3600 = 0 Reorder the terms: -3600 + -25x + x2 = 0 Solving -3600 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3600' to each side of the equation. -3600 + -25x + 3600 + x2 = 0 + 3600 Reorder the terms: -3600 + 3600 + -25x + x2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + -25x + x2 = 0 + 3600 -25x + x2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 -25x + x2 = 3600 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 = 3600 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 3600 + 156.25 Combine like terms: 3600 + 156.25 = 3756.25 156.25 + -25x + x2 = 3756.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 3756.25 Calculate the square root of the right side: 61.288253361 Break this problem into two subproblems by setting (x + -12.5) equal to 61.288253361 and -61.288253361.Subproblem 1
x + -12.5 = 61.288253361 Simplifying x + -12.5 = 61.288253361 Reorder the terms: -12.5 + x = 61.288253361 Solving -12.5 + x = 61.288253361 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 = 61.288253361 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 61.288253361 + 12.5 x = 61.288253361 + 12.5 Combine like terms: 61.288253361 + 12.5 = 73.788253361 x = 73.788253361 Simplifying x = 73.788253361Subproblem 2
x + -12.5 = -61.288253361 Simplifying x + -12.5 = -61.288253361 Reorder the terms: -12.5 + x = -61.288253361 Solving -12.5 + x = -61.288253361 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 = -61.288253361 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -61.288253361 + 12.5 x = -61.288253361 + 12.5 Combine like terms: -61.288253361 + 12.5 = -48.788253361 x = -48.788253361 Simplifying x = -48.788253361Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.788253361, -48.788253361}
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