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Simplifying 3x2 + 18x + -49 = 0 Reorder the terms: -49 + 18x + 3x2 = 0 Solving -49 + 18x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.33333333 + 6x + x2 = 0 Move the constant term to the right: Add '16.33333333' to each side of the equation. -16.33333333 + 6x + 16.33333333 + x2 = 0 + 16.33333333 Reorder the terms: -16.33333333 + 16.33333333 + 6x + x2 = 0 + 16.33333333 Combine like terms: -16.33333333 + 16.33333333 = 0.00000000 0.00000000 + 6x + x2 = 0 + 16.33333333 6x + x2 = 0 + 16.33333333 Combine like terms: 0 + 16.33333333 = 16.33333333 6x + x2 = 16.33333333 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 = 16.33333333 + 9 Reorder the terms: 9 + 6x + x2 = 16.33333333 + 9 Combine like terms: 16.33333333 + 9 = 25.33333333 9 + 6x + x2 = 25.33333333 Factor a perfect square on the left side: (x + 3)(x + 3) = 25.33333333 Calculate the square root of the right side: 5.033222957 Break this problem into two subproblems by setting (x + 3) equal to 5.033222957 and -5.033222957.Subproblem 1
x + 3 = 5.033222957 Simplifying x + 3 = 5.033222957 Reorder the terms: 3 + x = 5.033222957 Solving 3 + x = 5.033222957 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 = 5.033222957 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.033222957 + -3 x = 5.033222957 + -3 Combine like terms: 5.033222957 + -3 = 2.033222957 x = 2.033222957 Simplifying x = 2.033222957Subproblem 2
x + 3 = -5.033222957 Simplifying x + 3 = -5.033222957 Reorder the terms: 3 + x = -5.033222957 Solving 3 + x = -5.033222957 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 = -5.033222957 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.033222957 + -3 x = -5.033222957 + -3 Combine like terms: -5.033222957 + -3 = -8.033222957 x = -8.033222957 Simplifying x = -8.033222957Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.033222957, -8.033222957}
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