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Simplifying (3x + 6)(x + 4) = 400 Reorder the terms: (6 + 3x)(x + 4) = 400 Reorder the terms: (6 + 3x)(4 + x) = 400 Multiply (6 + 3x) * (4 + x) (6(4 + x) + 3x * (4 + x)) = 400 ((4 * 6 + x * 6) + 3x * (4 + x)) = 400 ((24 + 6x) + 3x * (4 + x)) = 400 (24 + 6x + (4 * 3x + x * 3x)) = 400 (24 + 6x + (12x + 3x2)) = 400 Combine like terms: 6x + 12x = 18x (24 + 18x + 3x2) = 400 Solving 24 + 18x + 3x2 = 400 Solving for variable 'x'. Reorder the terms: 24 + -400 + 18x + 3x2 = 400 + -400 Combine like terms: 24 + -400 = -376 -376 + 18x + 3x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -376 + 18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -125.3333333 + 6x + x2 = 0 Move the constant term to the right: Add '125.3333333' to each side of the equation. -125.3333333 + 6x + 125.3333333 + x2 = 0 + 125.3333333 Reorder the terms: -125.3333333 + 125.3333333 + 6x + x2 = 0 + 125.3333333 Combine like terms: -125.3333333 + 125.3333333 = 0.0000000 0.0000000 + 6x + x2 = 0 + 125.3333333 6x + x2 = 0 + 125.3333333 Combine like terms: 0 + 125.3333333 = 125.3333333 6x + x2 = 125.3333333 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 = 125.3333333 + 9 Reorder the terms: 9 + 6x + x2 = 125.3333333 + 9 Combine like terms: 125.3333333 + 9 = 134.3333333 9 + 6x + x2 = 134.3333333 Factor a perfect square on the left side: (x + 3)(x + 3) = 134.3333333 Calculate the square root of the right side: 11.590225766 Break this problem into two subproblems by setting (x + 3) equal to 11.590225766 and -11.590225766.Subproblem 1
x + 3 = 11.590225766 Simplifying x + 3 = 11.590225766 Reorder the terms: 3 + x = 11.590225766 Solving 3 + x = 11.590225766 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 = 11.590225766 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.590225766 + -3 x = 11.590225766 + -3 Combine like terms: 11.590225766 + -3 = 8.590225766 x = 8.590225766 Simplifying x = 8.590225766Subproblem 2
x + 3 = -11.590225766 Simplifying x + 3 = -11.590225766 Reorder the terms: 3 + x = -11.590225766 Solving 3 + x = -11.590225766 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 = -11.590225766 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.590225766 + -3 x = -11.590225766 + -3 Combine like terms: -11.590225766 + -3 = -14.590225766 x = -14.590225766 Simplifying x = -14.590225766Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.590225766, -14.590225766}
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