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Simplifying x2 + -5x = 220 Reorder the terms: -5x + x2 = 220 Solving -5x + x2 = 220 Solving for variable 'x'. Reorder the terms: -220 + -5x + x2 = 220 + -220 Combine like terms: 220 + -220 = 0 -220 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '220' to each side of the equation. -220 + -5x + 220 + x2 = 0 + 220 Reorder the terms: -220 + 220 + -5x + x2 = 0 + 220 Combine like terms: -220 + 220 = 0 0 + -5x + x2 = 0 + 220 -5x + x2 = 0 + 220 Combine like terms: 0 + 220 = 220 -5x + x2 = 220 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 220 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 220 + 6.25 Combine like terms: 220 + 6.25 = 226.25 6.25 + -5x + x2 = 226.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 226.25 Calculate the square root of the right side: 15.041608956 Break this problem into two subproblems by setting (x + -2.5) equal to 15.041608956 and -15.041608956.Subproblem 1
x + -2.5 = 15.041608956 Simplifying x + -2.5 = 15.041608956 Reorder the terms: -2.5 + x = 15.041608956 Solving -2.5 + x = 15.041608956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 15.041608956 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 15.041608956 + 2.5 x = 15.041608956 + 2.5 Combine like terms: 15.041608956 + 2.5 = 17.541608956 x = 17.541608956 Simplifying x = 17.541608956Subproblem 2
x + -2.5 = -15.041608956 Simplifying x + -2.5 = -15.041608956 Reorder the terms: -2.5 + x = -15.041608956 Solving -2.5 + x = -15.041608956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -15.041608956 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -15.041608956 + 2.5 x = -15.041608956 + 2.5 Combine like terms: -15.041608956 + 2.5 = -12.541608956 x = -12.541608956 Simplifying x = -12.541608956Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.541608956, -12.541608956}
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