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Simplifying 35 = (x + -3)(x + 2) Reorder the terms: 35 = (-3 + x)(x + 2) Reorder the terms: 35 = (-3 + x)(2 + x) Multiply (-3 + x) * (2 + x) 35 = (-3(2 + x) + x(2 + x)) 35 = ((2 * -3 + x * -3) + x(2 + x)) 35 = ((-6 + -3x) + x(2 + x)) 35 = (-6 + -3x + (2 * x + x * x)) 35 = (-6 + -3x + (2x + x2)) Combine like terms: -3x + 2x = -1x 35 = (-6 + -1x + x2) Solving 35 = -6 + -1x + x2 Solving for variable 'x'. Combine like terms: 35 + 6 = 41 41 + x + -1x2 = -6 + -1x + x2 + 6 + x + -1x2 Reorder the terms: 41 + x + -1x2 = -6 + 6 + -1x + x + x2 + -1x2 Combine like terms: -6 + 6 = 0 41 + x + -1x2 = 0 + -1x + x + x2 + -1x2 41 + x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 41 + x + -1x2 = 0 + x2 + -1x2 41 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 41 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -41 + -1x + x2 = 0 Move the constant term to the right: Add '41' to each side of the equation. -41 + -1x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + -1x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -1x + x2 = 0 + 41 -1x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 -1x + x2 = 41 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 41 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 41 + 0.25 Combine like terms: 41 + 0.25 = 41.25 0.25 + -1x + x2 = 41.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + 0.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + 0.5 = 6.422616289 Simplifying x + 0.5 = 6.422616289 Reorder the terms: 0.5 + x = 6.422616289 Solving 0.5 + x = 6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.422616289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.422616289 + -0.5 x = 6.422616289 + -0.5 Combine like terms: 6.422616289 + -0.5 = 5.922616289 x = 5.922616289 Simplifying x = 5.922616289Subproblem 2
x + 0.5 = -6.422616289 Simplifying x + 0.5 = -6.422616289 Reorder the terms: 0.5 + x = -6.422616289 Solving 0.5 + x = -6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.422616289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.422616289 + -0.5 x = -6.422616289 + -0.5 Combine like terms: -6.422616289 + -0.5 = -6.922616289 x = -6.922616289 Simplifying x = -6.922616289Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.922616289, -6.922616289}
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