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Simplifying x^{2}+ 6x + -65 = 0 Reorder the terms: -65 + 6x + x^{2}= 0 Solving -65 + 6x + x^{2}= 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + 6x + 65 + x^{2}= 0 + 65 Reorder the terms: -65 + 65 + 6x + x^{2}= 0 + 65 Combine like terms: -65 + 65 = 0 0 + 6x + x^{2}= 0 + 65 6x + x^{2}= 0 + 65 Combine like terms: 0 + 65 = 65 6x + x^{2}= 65 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 + x^{2}= 65 + 9 Reorder the terms: 9 + 6x + x^{2}= 65 + 9 Combine like terms: 65 + 9 = 74 9 + 6x + x^{2}= 74 Factor a perfect square on the left side: (x + 3)(x + 3) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (x + 3) equal to 8.602325267 and -8.602325267.## Subproblem 1

x + 3 = 8.602325267 Simplifying x + 3 = 8.602325267 Reorder the terms: 3 + x = 8.602325267 Solving 3 + x = 8.602325267 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 = 8.602325267 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.602325267 + -3 x = 8.602325267 + -3 Combine like terms: 8.602325267 + -3 = 5.602325267 x = 5.602325267 Simplifying x = 5.602325267## Subproblem 2

x + 3 = -8.602325267 Simplifying x + 3 = -8.602325267 Reorder the terms: 3 + x = -8.602325267 Solving 3 + x = -8.602325267 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 = -8.602325267 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.602325267 + -3 x = -8.602325267 + -3 Combine like terms: -8.602325267 + -3 = -11.602325267 x = -11.602325267 Simplifying x = -11.602325267## Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.602325267, -11.602325267}

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