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Simplifying x = x2 + -5x + -36 Reorder the terms: x = -36 + -5x + x2 Solving x = -36 + -5x + x2 Solving for variable 'x'. Reorder the terms: 36 + x + 5x + -1x2 = -36 + -5x + x2 + 36 + 5x + -1x2 Combine like terms: x + 5x = 6x 36 + 6x + -1x2 = -36 + -5x + x2 + 36 + 5x + -1x2 Reorder the terms: 36 + 6x + -1x2 = -36 + 36 + -5x + 5x + x2 + -1x2 Combine like terms: -36 + 36 = 0 36 + 6x + -1x2 = 0 + -5x + 5x + x2 + -1x2 36 + 6x + -1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 36 + 6x + -1x2 = 0 + x2 + -1x2 36 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 36 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + -6x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -6x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -6x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -6x + x2 = 0 + 36 -6x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -6x + x2 = 36 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 = 36 + 9 Reorder the terms: 9 + -6x + x2 = 36 + 9 Combine like terms: 36 + 9 = 45 9 + -6x + x2 = 45 Factor a perfect square on the left side: (x + -3)(x + -3) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -3) equal to 6.708203933 and -6.708203933.Subproblem 1
x + -3 = 6.708203933 Simplifying x + -3 = 6.708203933 Reorder the terms: -3 + x = 6.708203933 Solving -3 + x = 6.708203933 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 = 6.708203933 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.708203933 + 3 x = 6.708203933 + 3 Combine like terms: 6.708203933 + 3 = 9.708203933 x = 9.708203933 Simplifying x = 9.708203933Subproblem 2
x + -3 = -6.708203933 Simplifying x + -3 = -6.708203933 Reorder the terms: -3 + x = -6.708203933 Solving -3 + x = -6.708203933 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 = -6.708203933 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.708203933 + 3 x = -6.708203933 + 3 Combine like terms: -6.708203933 + 3 = -3.708203933 x = -3.708203933 Simplifying x = -3.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.708203933, -3.708203933}
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