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Simplifying 6x2 + 36x + 49 = 0 Reorder the terms: 49 + 36x + 6x2 = 0 Solving 49 + 36x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 8.166666667 + 6x + x2 = 0 Move the constant term to the right: Add '-8.166666667' to each side of the equation. 8.166666667 + 6x + -8.166666667 + x2 = 0 + -8.166666667 Reorder the terms: 8.166666667 + -8.166666667 + 6x + x2 = 0 + -8.166666667 Combine like terms: 8.166666667 + -8.166666667 = 0.000000000 0.000000000 + 6x + x2 = 0 + -8.166666667 6x + x2 = 0 + -8.166666667 Combine like terms: 0 + -8.166666667 = -8.166666667 6x + x2 = -8.166666667 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 = -8.166666667 + 9 Reorder the terms: 9 + 6x + x2 = -8.166666667 + 9 Combine like terms: -8.166666667 + 9 = 0.833333333 9 + 6x + x2 = 0.833333333 Factor a perfect square on the left side: (x + 3)(x + 3) = 0.833333333 Calculate the square root of the right side: 0.912870929 Break this problem into two subproblems by setting (x + 3) equal to 0.912870929 and -0.912870929.Subproblem 1
x + 3 = 0.912870929 Simplifying x + 3 = 0.912870929 Reorder the terms: 3 + x = 0.912870929 Solving 3 + x = 0.912870929 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 = 0.912870929 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0.912870929 + -3 x = 0.912870929 + -3 Combine like terms: 0.912870929 + -3 = -2.087129071 x = -2.087129071 Simplifying x = -2.087129071Subproblem 2
x + 3 = -0.912870929 Simplifying x + 3 = -0.912870929 Reorder the terms: 3 + x = -0.912870929 Solving 3 + x = -0.912870929 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 = -0.912870929 + -3 Combine like terms: 3 + -3 = 0 0 + x = -0.912870929 + -3 x = -0.912870929 + -3 Combine like terms: -0.912870929 + -3 = -3.912870929 x = -3.912870929 Simplifying x = -3.912870929Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.087129071, -3.912870929}
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