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Simplifying x2 + 6x + -306 = 0 Reorder the terms: -306 + 6x + x2 = 0 Solving -306 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '306' to each side of the equation. -306 + 6x + 306 + x2 = 0 + 306 Reorder the terms: -306 + 306 + 6x + x2 = 0 + 306 Combine like terms: -306 + 306 = 0 0 + 6x + x2 = 0 + 306 6x + x2 = 0 + 306 Combine like terms: 0 + 306 = 306 6x + x2 = 306 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 = 306 + 9 Reorder the terms: 9 + 6x + x2 = 306 + 9 Combine like terms: 306 + 9 = 315 9 + 6x + x2 = 315 Factor a perfect square on the left side: (x + 3)(x + 3) = 315 Calculate the square root of the right side: 17.748239349 Break this problem into two subproblems by setting (x + 3) equal to 17.748239349 and -17.748239349.Subproblem 1
x + 3 = 17.748239349 Simplifying x + 3 = 17.748239349 Reorder the terms: 3 + x = 17.748239349 Solving 3 + x = 17.748239349 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 = 17.748239349 + -3 Combine like terms: 3 + -3 = 0 0 + x = 17.748239349 + -3 x = 17.748239349 + -3 Combine like terms: 17.748239349 + -3 = 14.748239349 x = 14.748239349 Simplifying x = 14.748239349Subproblem 2
x + 3 = -17.748239349 Simplifying x + 3 = -17.748239349 Reorder the terms: 3 + x = -17.748239349 Solving 3 + x = -17.748239349 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 = -17.748239349 + -3 Combine like terms: 3 + -3 = 0 0 + x = -17.748239349 + -3 x = -17.748239349 + -3 Combine like terms: -17.748239349 + -3 = -20.748239349 x = -20.748239349 Simplifying x = -20.748239349Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.748239349, -20.748239349}
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