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Simplifying x2 + 6x + -344 = 0 Reorder the terms: -344 + 6x + x2 = 0 Solving -344 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '344' to each side of the equation. -344 + 6x + 344 + x2 = 0 + 344 Reorder the terms: -344 + 344 + 6x + x2 = 0 + 344 Combine like terms: -344 + 344 = 0 0 + 6x + x2 = 0 + 344 6x + x2 = 0 + 344 Combine like terms: 0 + 344 = 344 6x + x2 = 344 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 = 344 + 9 Reorder the terms: 9 + 6x + x2 = 344 + 9 Combine like terms: 344 + 9 = 353 9 + 6x + x2 = 353 Factor a perfect square on the left side: (x + 3)(x + 3) = 353 Calculate the square root of the right side: 18.788294228 Break this problem into two subproblems by setting (x + 3) equal to 18.788294228 and -18.788294228.Subproblem 1
x + 3 = 18.788294228 Simplifying x + 3 = 18.788294228 Reorder the terms: 3 + x = 18.788294228 Solving 3 + x = 18.788294228 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 = 18.788294228 + -3 Combine like terms: 3 + -3 = 0 0 + x = 18.788294228 + -3 x = 18.788294228 + -3 Combine like terms: 18.788294228 + -3 = 15.788294228 x = 15.788294228 Simplifying x = 15.788294228Subproblem 2
x + 3 = -18.788294228 Simplifying x + 3 = -18.788294228 Reorder the terms: 3 + x = -18.788294228 Solving 3 + x = -18.788294228 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 = -18.788294228 + -3 Combine like terms: 3 + -3 = 0 0 + x = -18.788294228 + -3 x = -18.788294228 + -3 Combine like terms: -18.788294228 + -3 = -21.788294228 x = -21.788294228 Simplifying x = -21.788294228Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.788294228, -21.788294228}
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