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Simplifying x2 + 6x = 324 Reorder the terms: 6x + x2 = 324 Solving 6x + x2 = 324 Solving for variable 'x'. Reorder the terms: -324 + 6x + x2 = 324 + -324 Combine like terms: 324 + -324 = 0 -324 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '324' to each side of the equation. -324 + 6x + 324 + x2 = 0 + 324 Reorder the terms: -324 + 324 + 6x + x2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + 6x + x2 = 0 + 324 6x + x2 = 0 + 324 Combine like terms: 0 + 324 = 324 6x + x2 = 324 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 = 324 + 9 Reorder the terms: 9 + 6x + x2 = 324 + 9 Combine like terms: 324 + 9 = 333 9 + 6x + x2 = 333 Factor a perfect square on the left side: (x + 3)(x + 3) = 333 Calculate the square root of the right side: 18.248287591 Break this problem into two subproblems by setting (x + 3) equal to 18.248287591 and -18.248287591.Subproblem 1
x + 3 = 18.248287591 Simplifying x + 3 = 18.248287591 Reorder the terms: 3 + x = 18.248287591 Solving 3 + x = 18.248287591 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 = 18.248287591 + -3 Combine like terms: 3 + -3 = 0 0 + x = 18.248287591 + -3 x = 18.248287591 + -3 Combine like terms: 18.248287591 + -3 = 15.248287591 x = 15.248287591 Simplifying x = 15.248287591Subproblem 2
x + 3 = -18.248287591 Simplifying x + 3 = -18.248287591 Reorder the terms: 3 + x = -18.248287591 Solving 3 + x = -18.248287591 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 = -18.248287591 + -3 Combine like terms: 3 + -3 = 0 0 + x = -18.248287591 + -3 x = -18.248287591 + -3 Combine like terms: -18.248287591 + -3 = -21.248287591 x = -21.248287591 Simplifying x = -21.248287591Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.248287591, -21.248287591}
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