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Simplifying x2 + -5x = 35 Reorder the terms: -5x + x2 = 35 Solving -5x + x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + -5x + x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -5x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -5x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -5x + x2 = 0 + 35 -5x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -5x + x2 = 35 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 = 35 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 35 + 6.25 Combine like terms: 35 + 6.25 = 41.25 6.25 + -5x + x2 = 41.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + -2.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + -2.5 = 6.422616289 Simplifying x + -2.5 = 6.422616289 Reorder the terms: -2.5 + x = 6.422616289 Solving -2.5 + x = 6.422616289 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 = 6.422616289 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 6.422616289 + 2.5 x = 6.422616289 + 2.5 Combine like terms: 6.422616289 + 2.5 = 8.922616289 x = 8.922616289 Simplifying x = 8.922616289Subproblem 2
x + -2.5 = -6.422616289 Simplifying x + -2.5 = -6.422616289 Reorder the terms: -2.5 + x = -6.422616289 Solving -2.5 + x = -6.422616289 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 = -6.422616289 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -6.422616289 + 2.5 x = -6.422616289 + 2.5 Combine like terms: -6.422616289 + 2.5 = -3.922616289 x = -3.922616289 Simplifying x = -3.922616289Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.922616289, -3.922616289}
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