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Simplifying x2 + 6x = 5743 Reorder the terms: 6x + x2 = 5743 Solving 6x + x2 = 5743 Solving for variable 'x'. Reorder the terms: -5743 + 6x + x2 = 5743 + -5743 Combine like terms: 5743 + -5743 = 0 -5743 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5743' to each side of the equation. -5743 + 6x + 5743 + x2 = 0 + 5743 Reorder the terms: -5743 + 5743 + 6x + x2 = 0 + 5743 Combine like terms: -5743 + 5743 = 0 0 + 6x + x2 = 0 + 5743 6x + x2 = 0 + 5743 Combine like terms: 0 + 5743 = 5743 6x + x2 = 5743 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 5743 + 9 Reorder the terms: 9 + 6x + x2 = 5743 + 9 Combine like terms: 5743 + 9 = 5752 9 + 6x + x2 = 5752 Factor a perfect square on the left side: (x + 3)(x + 3) = 5752 Calculate the square root of the right side: 75.841940903 Break this problem into two subproblems by setting (x + 3) equal to 75.841940903 and -75.841940903.Subproblem 1
x + 3 = 75.841940903 Simplifying x + 3 = 75.841940903 Reorder the terms: 3 + x = 75.841940903 Solving 3 + x = 75.841940903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 75.841940903 + -3 Combine like terms: 3 + -3 = 0 0 + x = 75.841940903 + -3 x = 75.841940903 + -3 Combine like terms: 75.841940903 + -3 = 72.841940903 x = 72.841940903 Simplifying x = 72.841940903Subproblem 2
x + 3 = -75.841940903 Simplifying x + 3 = -75.841940903 Reorder the terms: 3 + x = -75.841940903 Solving 3 + x = -75.841940903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -75.841940903 + -3 Combine like terms: 3 + -3 = 0 0 + x = -75.841940903 + -3 x = -75.841940903 + -3 Combine like terms: -75.841940903 + -3 = -78.841940903 x = -78.841940903 Simplifying x = -78.841940903Solution
The solution to the problem is based on the solutions from the subproblems. x = {72.841940903, -78.841940903}
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