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Simplifying x2 + -25x + -144 = 0 Reorder the terms: -144 + -25x + x2 = 0 Solving -144 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -25x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -25x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -25x + x2 = 0 + 144 -25x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -25x + x2 = 144 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 = 144 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 144 + 156.25 Combine like terms: 144 + 156.25 = 300.25 156.25 + -25x + x2 = 300.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 300.25 Calculate the square root of the right side: 17.327723451 Break this problem into two subproblems by setting (x + -12.5) equal to 17.327723451 and -17.327723451.Subproblem 1
x + -12.5 = 17.327723451 Simplifying x + -12.5 = 17.327723451 Reorder the terms: -12.5 + x = 17.327723451 Solving -12.5 + x = 17.327723451 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 = 17.327723451 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 17.327723451 + 12.5 x = 17.327723451 + 12.5 Combine like terms: 17.327723451 + 12.5 = 29.827723451 x = 29.827723451 Simplifying x = 29.827723451Subproblem 2
x + -12.5 = -17.327723451 Simplifying x + -12.5 = -17.327723451 Reorder the terms: -12.5 + x = -17.327723451 Solving -12.5 + x = -17.327723451 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 = -17.327723451 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -17.327723451 + 12.5 x = -17.327723451 + 12.5 Combine like terms: -17.327723451 + 12.5 = -4.827723451 x = -4.827723451 Simplifying x = -4.827723451Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.827723451, -4.827723451}
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