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Simplifying 2x2 + 24x + 57 = 0 Reorder the terms: 57 + 24x + 2x2 = 0 Solving 57 + 24x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 28.5 + 12x + x2 = 0 Move the constant term to the right: Add '-28.5' to each side of the equation. 28.5 + 12x + -28.5 + x2 = 0 + -28.5 Reorder the terms: 28.5 + -28.5 + 12x + x2 = 0 + -28.5 Combine like terms: 28.5 + -28.5 = 0.0 0.0 + 12x + x2 = 0 + -28.5 12x + x2 = 0 + -28.5 Combine like terms: 0 + -28.5 = -28.5 12x + x2 = -28.5 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -28.5 + 36 Reorder the terms: 36 + 12x + x2 = -28.5 + 36 Combine like terms: -28.5 + 36 = 7.5 36 + 12x + x2 = 7.5 Factor a perfect square on the left side: (x + 6)(x + 6) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (x + 6) equal to 2.738612788 and -2.738612788.Subproblem 1
x + 6 = 2.738612788 Simplifying x + 6 = 2.738612788 Reorder the terms: 6 + x = 2.738612788 Solving 6 + x = 2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 2.738612788 + -6 Combine like terms: 6 + -6 = 0 0 + x = 2.738612788 + -6 x = 2.738612788 + -6 Combine like terms: 2.738612788 + -6 = -3.261387212 x = -3.261387212 Simplifying x = -3.261387212Subproblem 2
x + 6 = -2.738612788 Simplifying x + 6 = -2.738612788 Reorder the terms: 6 + x = -2.738612788 Solving 6 + x = -2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -2.738612788 + -6 Combine like terms: 6 + -6 = 0 0 + x = -2.738612788 + -6 x = -2.738612788 + -6 Combine like terms: -2.738612788 + -6 = -8.738612788 x = -8.738612788 Simplifying x = -8.738612788Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.261387212, -8.738612788}
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