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Simplifying x2 + 54x + 624 = 0 Reorder the terms: 624 + 54x + x2 = 0 Solving 624 + 54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-624' to each side of the equation. 624 + 54x + -624 + x2 = 0 + -624 Reorder the terms: 624 + -624 + 54x + x2 = 0 + -624 Combine like terms: 624 + -624 = 0 0 + 54x + x2 = 0 + -624 54x + x2 = 0 + -624 Combine like terms: 0 + -624 = -624 54x + x2 = -624 The x term is 54x. Take half its coefficient (27). Square it (729) and add it to both sides. Add '729' to each side of the equation. 54x + 729 + x2 = -624 + 729 Reorder the terms: 729 + 54x + x2 = -624 + 729 Combine like terms: -624 + 729 = 105 729 + 54x + x2 = 105 Factor a perfect square on the left side: (x + 27)(x + 27) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + 27) equal to 10.246950766 and -10.246950766.Subproblem 1
x + 27 = 10.246950766 Simplifying x + 27 = 10.246950766 Reorder the terms: 27 + x = 10.246950766 Solving 27 + x = 10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = 10.246950766 + -27 Combine like terms: 27 + -27 = 0 0 + x = 10.246950766 + -27 x = 10.246950766 + -27 Combine like terms: 10.246950766 + -27 = -16.753049234 x = -16.753049234 Simplifying x = -16.753049234Subproblem 2
x + 27 = -10.246950766 Simplifying x + 27 = -10.246950766 Reorder the terms: 27 + x = -10.246950766 Solving 27 + x = -10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = -10.246950766 + -27 Combine like terms: 27 + -27 = 0 0 + x = -10.246950766 + -27 x = -10.246950766 + -27 Combine like terms: -10.246950766 + -27 = -37.246950766 x = -37.246950766 Simplifying x = -37.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-16.753049234, -37.246950766}
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