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Simplifying 336 = x2 + 6x Reorder the terms: 336 = 6x + x2 Solving 336 = 6x + x2 Solving for variable 'x'. Reorder the terms: 336 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 336 + -6x + -1x2 = 0 + x2 + -1x2 336 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 336 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -336 + 6x + x2 = 0 Move the constant term to the right: Add '336' to each side of the equation. -336 + 6x + 336 + x2 = 0 + 336 Reorder the terms: -336 + 336 + 6x + x2 = 0 + 336 Combine like terms: -336 + 336 = 0 0 + 6x + x2 = 0 + 336 6x + x2 = 0 + 336 Combine like terms: 0 + 336 = 336 6x + x2 = 336 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 = 336 + 9 Reorder the terms: 9 + 6x + x2 = 336 + 9 Combine like terms: 336 + 9 = 345 9 + 6x + x2 = 345 Factor a perfect square on the left side: (x + 3)(x + 3) = 345 Calculate the square root of the right side: 18.574175621 Break this problem into two subproblems by setting (x + 3) equal to 18.574175621 and -18.574175621.Subproblem 1
x + 3 = 18.574175621 Simplifying x + 3 = 18.574175621 Reorder the terms: 3 + x = 18.574175621 Solving 3 + x = 18.574175621 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 = 18.574175621 + -3 Combine like terms: 3 + -3 = 0 0 + x = 18.574175621 + -3 x = 18.574175621 + -3 Combine like terms: 18.574175621 + -3 = 15.574175621 x = 15.574175621 Simplifying x = 15.574175621Subproblem 2
x + 3 = -18.574175621 Simplifying x + 3 = -18.574175621 Reorder the terms: 3 + x = -18.574175621 Solving 3 + x = -18.574175621 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 = -18.574175621 + -3 Combine like terms: 3 + -3 = 0 0 + x = -18.574175621 + -3 x = -18.574175621 + -3 Combine like terms: -18.574175621 + -3 = -21.574175621 x = -21.574175621 Simplifying x = -21.574175621Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.574175621, -21.574175621}
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