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Simplifying x2 + 6x + -305 = 0 Reorder the terms: -305 + 6x + x2 = 0 Solving -305 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '305' to each side of the equation. -305 + 6x + 305 + x2 = 0 + 305 Reorder the terms: -305 + 305 + 6x + x2 = 0 + 305 Combine like terms: -305 + 305 = 0 0 + 6x + x2 = 0 + 305 6x + x2 = 0 + 305 Combine like terms: 0 + 305 = 305 6x + x2 = 305 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 = 305 + 9 Reorder the terms: 9 + 6x + x2 = 305 + 9 Combine like terms: 305 + 9 = 314 9 + 6x + x2 = 314 Factor a perfect square on the left side: (x + 3)(x + 3) = 314 Calculate the square root of the right side: 17.720045147 Break this problem into two subproblems by setting (x + 3) equal to 17.720045147 and -17.720045147.Subproblem 1
x + 3 = 17.720045147 Simplifying x + 3 = 17.720045147 Reorder the terms: 3 + x = 17.720045147 Solving 3 + x = 17.720045147 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 = 17.720045147 + -3 Combine like terms: 3 + -3 = 0 0 + x = 17.720045147 + -3 x = 17.720045147 + -3 Combine like terms: 17.720045147 + -3 = 14.720045147 x = 14.720045147 Simplifying x = 14.720045147Subproblem 2
x + 3 = -17.720045147 Simplifying x + 3 = -17.720045147 Reorder the terms: 3 + x = -17.720045147 Solving 3 + x = -17.720045147 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 = -17.720045147 + -3 Combine like terms: 3 + -3 = 0 0 + x = -17.720045147 + -3 x = -17.720045147 + -3 Combine like terms: -17.720045147 + -3 = -20.720045147 x = -20.720045147 Simplifying x = -20.720045147Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.720045147, -20.720045147}
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