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Simplifying x2 + -80x + 25 = 0 Reorder the terms: 25 + -80x + x2 = 0 Solving 25 + -80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -80x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -80x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -80x + x2 = 0 + -25 -80x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -80x + x2 = -25 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = -25 + 1600 Reorder the terms: 1600 + -80x + x2 = -25 + 1600 Combine like terms: -25 + 1600 = 1575 1600 + -80x + x2 = 1575 Factor a perfect square on the left side: (x + -40)(x + -40) = 1575 Calculate the square root of the right side: 39.686269666 Break this problem into two subproblems by setting (x + -40) equal to 39.686269666 and -39.686269666.Subproblem 1
x + -40 = 39.686269666 Simplifying x + -40 = 39.686269666 Reorder the terms: -40 + x = 39.686269666 Solving -40 + x = 39.686269666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 39.686269666 + 40 Combine like terms: -40 + 40 = 0 0 + x = 39.686269666 + 40 x = 39.686269666 + 40 Combine like terms: 39.686269666 + 40 = 79.686269666 x = 79.686269666 Simplifying x = 79.686269666Subproblem 2
x + -40 = -39.686269666 Simplifying x + -40 = -39.686269666 Reorder the terms: -40 + x = -39.686269666 Solving -40 + x = -39.686269666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -39.686269666 + 40 Combine like terms: -40 + 40 = 0 0 + x = -39.686269666 + 40 x = -39.686269666 + 40 Combine like terms: -39.686269666 + 40 = 0.313730334 x = 0.313730334 Simplifying x = 0.313730334Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.686269666, 0.313730334}
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