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Simplifying x + 0.25x(x + -54) = 180 Reorder the terms: x + 0.25x(-54 + x) = 180 x + (-54 * 0.25x + x * 0.25x) = 180 x + (-13.5x + 0.25x2) = 180 Combine like terms: x + -13.5x = -12.5x -12.5x + 0.25x2 = 180 Solving -12.5x + 0.25x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -12.5x + 0.25x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -12.5x + 0.25x2 = 0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -720 + -50x + x2 = 0 Move the constant term to the right: Add '720' to each side of the equation. -720 + -50x + 720 + x2 = 0 + 720 Reorder the terms: -720 + 720 + -50x + x2 = 0 + 720 Combine like terms: -720 + 720 = 0 0 + -50x + x2 = 0 + 720 -50x + x2 = 0 + 720 Combine like terms: 0 + 720 = 720 -50x + x2 = 720 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 720 + 625 Reorder the terms: 625 + -50x + x2 = 720 + 625 Combine like terms: 720 + 625 = 1345 625 + -50x + x2 = 1345 Factor a perfect square on the left side: (x + -25)(x + -25) = 1345 Calculate the square root of the right side: 36.674241642 Break this problem into two subproblems by setting (x + -25) equal to 36.674241642 and -36.674241642.Subproblem 1
x + -25 = 36.674241642 Simplifying x + -25 = 36.674241642 Reorder the terms: -25 + x = 36.674241642 Solving -25 + x = 36.674241642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 36.674241642 + 25 Combine like terms: -25 + 25 = 0 0 + x = 36.674241642 + 25 x = 36.674241642 + 25 Combine like terms: 36.674241642 + 25 = 61.674241642 x = 61.674241642 Simplifying x = 61.674241642Subproblem 2
x + -25 = -36.674241642 Simplifying x + -25 = -36.674241642 Reorder the terms: -25 + x = -36.674241642 Solving -25 + x = -36.674241642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -36.674241642 + 25 Combine like terms: -25 + 25 = 0 0 + x = -36.674241642 + 25 x = -36.674241642 + 25 Combine like terms: -36.674241642 + 25 = -11.674241642 x = -11.674241642 Simplifying x = -11.674241642Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.674241642, -11.674241642}
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