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Simplifying x2 + 6x = 57 Reorder the terms: 6x + x2 = 57 Solving 6x + x2 = 57 Solving for variable 'x'. Reorder the terms: -57 + 6x + x2 = 57 + -57 Combine like terms: 57 + -57 = 0 -57 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '57' to each side of the equation. -57 + 6x + 57 + x2 = 0 + 57 Reorder the terms: -57 + 57 + 6x + x2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + 6x + x2 = 0 + 57 6x + x2 = 0 + 57 Combine like terms: 0 + 57 = 57 6x + x2 = 57 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 = 57 + 9 Reorder the terms: 9 + 6x + x2 = 57 + 9 Combine like terms: 57 + 9 = 66 9 + 6x + x2 = 66 Factor a perfect square on the left side: (x + 3)(x + 3) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (x + 3) equal to 8.124038405 and -8.124038405.Subproblem 1
x + 3 = 8.124038405 Simplifying x + 3 = 8.124038405 Reorder the terms: 3 + x = 8.124038405 Solving 3 + x = 8.124038405 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 = 8.124038405 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.124038405 + -3 x = 8.124038405 + -3 Combine like terms: 8.124038405 + -3 = 5.124038405 x = 5.124038405 Simplifying x = 5.124038405Subproblem 2
x + 3 = -8.124038405 Simplifying x + 3 = -8.124038405 Reorder the terms: 3 + x = -8.124038405 Solving 3 + x = -8.124038405 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 = -8.124038405 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.124038405 + -3 x = -8.124038405 + -3 Combine like terms: -8.124038405 + -3 = -11.124038405 x = -11.124038405 Simplifying x = -11.124038405Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.124038405, -11.124038405}
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