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Simplifying x2 + 4x + -36 = 0 Reorder the terms: -36 + 4x + x2 = 0 Solving -36 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 4x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 4x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 4x + x2 = 0 + 36 4x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 4x + x2 = 36 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 36 + 4 Reorder the terms: 4 + 4x + x2 = 36 + 4 Combine like terms: 36 + 4 = 40 4 + 4x + x2 = 40 Factor a perfect square on the left side: (x + 2)(x + 2) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + 2) equal to 6.32455532 and -6.32455532.Subproblem 1
x + 2 = 6.32455532 Simplifying x + 2 = 6.32455532 Reorder the terms: 2 + x = 6.32455532 Solving 2 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 6.32455532 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.32455532 + -2 x = 6.32455532 + -2 Combine like terms: 6.32455532 + -2 = 4.32455532 x = 4.32455532 Simplifying x = 4.32455532Subproblem 2
x + 2 = -6.32455532 Simplifying x + 2 = -6.32455532 Reorder the terms: 2 + x = -6.32455532 Solving 2 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -6.32455532 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.32455532 + -2 x = -6.32455532 + -2 Combine like terms: -6.32455532 + -2 = -8.32455532 x = -8.32455532 Simplifying x = -8.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.32455532, -8.32455532}
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