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Simplifying ((3 + x)(3 + x)) = 96 Multiply (3 + x) * (3 + x) ((3(3 + x) + x(3 + x))) = 96 (((3 * 3 + x * 3) + x(3 + x))) = 96 (((9 + 3x) + x(3 + x))) = 96 ((9 + 3x + (3 * x + x * x))) = 96 ((9 + 3x + (3x + x2))) = 96 Combine like terms: 3x + 3x = 6x ((9 + 6x + x2)) = 96 (9 + 6x + x2) = 96 Remove parenthesis around (9 + 6x + x2) 9 + 6x + x2 = 96 Solving 9 + 6x + x2 = 96 Solving for variable 'x'. Reorder the terms: 9 + -96 + 6x + x2 = 96 + -96 Combine like terms: 9 + -96 = -87 -87 + 6x + x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -87 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '87' to each side of the equation. -87 + 6x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + 6x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + 6x + x2 = 0 + 87 6x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 6x + x2 = 87 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 = 87 + 9 Reorder the terms: 9 + 6x + x2 = 87 + 9 Combine like terms: 87 + 9 = 96 9 + 6x + x2 = 96 Factor a perfect square on the left side: (x + 3)(x + 3) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + 3) equal to 9.797958971 and -9.797958971.Subproblem 1
x + 3 = 9.797958971 Simplifying x + 3 = 9.797958971 Reorder the terms: 3 + x = 9.797958971 Solving 3 + x = 9.797958971 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 = 9.797958971 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.797958971 + -3 x = 9.797958971 + -3 Combine like terms: 9.797958971 + -3 = 6.797958971 x = 6.797958971 Simplifying x = 6.797958971Subproblem 2
x + 3 = -9.797958971 Simplifying x + 3 = -9.797958971 Reorder the terms: 3 + x = -9.797958971 Solving 3 + x = -9.797958971 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 = -9.797958971 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.797958971 + -3 x = -9.797958971 + -3 Combine like terms: -9.797958971 + -3 = -12.797958971 x = -12.797958971 Simplifying x = -12.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.797958971, -12.797958971}
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