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Simplifying 216 = x2 + 6x + 8 Reorder the terms: 216 = 8 + 6x + x2 Solving 216 = 8 + 6x + x2 Solving for variable 'x'. Combine like terms: 216 + -8 = 208 208 + -6x + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2 Reorder the terms: 208 + -6x + -1x2 = 8 + -8 + 6x + -6x + x2 + -1x2 Combine like terms: 8 + -8 = 0 208 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 208 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 208 + -6x + -1x2 = 0 + x2 + -1x2 208 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 208 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -208 + 6x + x2 = 0 Move the constant term to the right: Add '208' to each side of the equation. -208 + 6x + 208 + x2 = 0 + 208 Reorder the terms: -208 + 208 + 6x + x2 = 0 + 208 Combine like terms: -208 + 208 = 0 0 + 6x + x2 = 0 + 208 6x + x2 = 0 + 208 Combine like terms: 0 + 208 = 208 6x + x2 = 208 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 = 208 + 9 Reorder the terms: 9 + 6x + x2 = 208 + 9 Combine like terms: 208 + 9 = 217 9 + 6x + x2 = 217 Factor a perfect square on the left side: (x + 3)(x + 3) = 217 Calculate the square root of the right side: 14.730919863 Break this problem into two subproblems by setting (x + 3) equal to 14.730919863 and -14.730919863.Subproblem 1
x + 3 = 14.730919863 Simplifying x + 3 = 14.730919863 Reorder the terms: 3 + x = 14.730919863 Solving 3 + x = 14.730919863 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 = 14.730919863 + -3 Combine like terms: 3 + -3 = 0 0 + x = 14.730919863 + -3 x = 14.730919863 + -3 Combine like terms: 14.730919863 + -3 = 11.730919863 x = 11.730919863 Simplifying x = 11.730919863Subproblem 2
x + 3 = -14.730919863 Simplifying x + 3 = -14.730919863 Reorder the terms: 3 + x = -14.730919863 Solving 3 + x = -14.730919863 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 = -14.730919863 + -3 Combine like terms: 3 + -3 = 0 0 + x = -14.730919863 + -3 x = -14.730919863 + -3 Combine like terms: -14.730919863 + -3 = -17.730919863 x = -17.730919863 Simplifying x = -17.730919863Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.730919863, -17.730919863}
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