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Simplifying (x + 3)(x + 3) = 48 Reorder the terms: (3 + x)(x + 3) = 48 Reorder the terms: (3 + x)(3 + x) = 48 Multiply (3 + x) * (3 + x) (3(3 + x) + x(3 + x)) = 48 ((3 * 3 + x * 3) + x(3 + x)) = 48 ((9 + 3x) + x(3 + x)) = 48 (9 + 3x + (3 * x + x * x)) = 48 (9 + 3x + (3x + x2)) = 48 Combine like terms: 3x + 3x = 6x (9 + 6x + x2) = 48 Solving 9 + 6x + x2 = 48 Solving for variable 'x'. Reorder the terms: 9 + -48 + 6x + x2 = 48 + -48 Combine like terms: 9 + -48 = -39 -39 + 6x + x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -39 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 6x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 6x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 6x + x2 = 0 + 39 6x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 6x + x2 = 39 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 = 39 + 9 Reorder the terms: 9 + 6x + x2 = 39 + 9 Combine like terms: 39 + 9 = 48 9 + 6x + x2 = 48 Factor a perfect square on the left side: (x + 3)(x + 3) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + 3) equal to 6.92820323 and -6.92820323.Subproblem 1
x + 3 = 6.92820323 Simplifying x + 3 = 6.92820323 Reorder the terms: 3 + x = 6.92820323 Solving 3 + x = 6.92820323 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 = 6.92820323 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.92820323 + -3 x = 6.92820323 + -3 Combine like terms: 6.92820323 + -3 = 3.92820323 x = 3.92820323 Simplifying x = 3.92820323Subproblem 2
x + 3 = -6.92820323 Simplifying x + 3 = -6.92820323 Reorder the terms: 3 + x = -6.92820323 Solving 3 + x = -6.92820323 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 = -6.92820323 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.92820323 + -3 x = -6.92820323 + -3 Combine like terms: -6.92820323 + -3 = -9.92820323 x = -9.92820323 Simplifying x = -9.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.92820323, -9.92820323}
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