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Simplifying x2 + -25x = 180 Reorder the terms: -25x + x2 = 180 Solving -25x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -25x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -25x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -25x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -25x + x2 = 0 + 180 -25x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -25x + x2 = 180 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 = 180 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 180 + 156.25 Combine like terms: 180 + 156.25 = 336.25 156.25 + -25x + x2 = 336.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 336.25 Calculate the square root of the right side: 18.337120821 Break this problem into two subproblems by setting (x + -12.5) equal to 18.337120821 and -18.337120821.Subproblem 1
x + -12.5 = 18.337120821 Simplifying x + -12.5 = 18.337120821 Reorder the terms: -12.5 + x = 18.337120821 Solving -12.5 + x = 18.337120821 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 = 18.337120821 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 18.337120821 + 12.5 x = 18.337120821 + 12.5 Combine like terms: 18.337120821 + 12.5 = 30.837120821 x = 30.837120821 Simplifying x = 30.837120821Subproblem 2
x + -12.5 = -18.337120821 Simplifying x + -12.5 = -18.337120821 Reorder the terms: -12.5 + x = -18.337120821 Solving -12.5 + x = -18.337120821 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 = -18.337120821 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -18.337120821 + 12.5 x = -18.337120821 + 12.5 Combine like terms: -18.337120821 + 12.5 = -5.837120821 x = -5.837120821 Simplifying x = -5.837120821Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.837120821, -5.837120821}
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