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Simplifying 57 = (x(x + 6)) Reorder the terms: 57 = (x(6 + x)) 57 = ((6 * x + x * x)) 57 = ((6x + x2)) 57 = (6x + x2) Remove parenthesis around (6x + x2) 57 = 6x + x2 Solving 57 = 6x + x2 Solving for variable 'x'. Reorder the terms: 57 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 57 + -6x + -1x2 = 0 + x2 + -1x2 57 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 57 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -57 + 6x + x2 = 0 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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