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Simplifying x2 + -6x + -57 = 0 Reorder the terms: -57 + -6x + x2 = 0 Solving -57 + -6x + x2 = 0 Solving for variable 'x'. 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 = 11.124038405 x = 11.124038405 Simplifying x = 11.124038405Subproblem 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 = -5.124038405 x = -5.124038405 Simplifying x = -5.124038405Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.124038405, -5.124038405}
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