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Simplifying (x + 3)(x + 3) + 6 = 81 Reorder the terms: (3 + x)(x + 3) + 6 = 81 Reorder the terms: (3 + x)(3 + x) + 6 = 81 Multiply (3 + x) * (3 + x) (3(3 + x) + x(3 + x)) + 6 = 81 ((3 * 3 + x * 3) + x(3 + x)) + 6 = 81 ((9 + 3x) + x(3 + x)) + 6 = 81 (9 + 3x + (3 * x + x * x)) + 6 = 81 (9 + 3x + (3x + x2)) + 6 = 81 Combine like terms: 3x + 3x = 6x (9 + 6x + x2) + 6 = 81 Reorder the terms: 9 + 6 + 6x + x2 = 81 Combine like terms: 9 + 6 = 15 15 + 6x + x2 = 81 Solving 15 + 6x + x2 = 81 Solving for variable 'x'. Reorder the terms: 15 + -81 + 6x + x2 = 81 + -81 Combine like terms: 15 + -81 = -66 -66 + 6x + x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -66 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + 6x + 66 + x2 = 0 + 66 Reorder the terms: -66 + 66 + 6x + x2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 6x + x2 = 0 + 66 6x + x2 = 0 + 66 Combine like terms: 0 + 66 = 66 6x + x2 = 66 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 = 66 + 9 Reorder the terms: 9 + 6x + x2 = 66 + 9 Combine like terms: 66 + 9 = 75 9 + 6x + x2 = 75 Factor a perfect square on the left side: (x + 3)(x + 3) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + 3) equal to 8.660254038 and -8.660254038.Subproblem 1
x + 3 = 8.660254038 Simplifying x + 3 = 8.660254038 Reorder the terms: 3 + x = 8.660254038 Solving 3 + x = 8.660254038 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 = 8.660254038 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.660254038 + -3 x = 8.660254038 + -3 Combine like terms: 8.660254038 + -3 = 5.660254038 x = 5.660254038 Simplifying x = 5.660254038Subproblem 2
x + 3 = -8.660254038 Simplifying x + 3 = -8.660254038 Reorder the terms: 3 + x = -8.660254038 Solving 3 + x = -8.660254038 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 = -8.660254038 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.660254038 + -3 x = -8.660254038 + -3 Combine like terms: -8.660254038 + -3 = -11.660254038 x = -11.660254038 Simplifying x = -11.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.660254038, -11.660254038}
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