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Simplifying (16 + 2x)(12 + 2x) = 369 Multiply (16 + 2x) * (12 + 2x) (16(12 + 2x) + 2x * (12 + 2x)) = 369 ((12 * 16 + 2x * 16) + 2x * (12 + 2x)) = 369 ((192 + 32x) + 2x * (12 + 2x)) = 369 (192 + 32x + (12 * 2x + 2x * 2x)) = 369 (192 + 32x + (24x + 4x2)) = 369 Combine like terms: 32x + 24x = 56x (192 + 56x + 4x2) = 369 Solving 192 + 56x + 4x2 = 369 Solving for variable 'x'. Reorder the terms: 192 + -369 + 56x + 4x2 = 369 + -369 Combine like terms: 192 + -369 = -177 -177 + 56x + 4x2 = 369 + -369 Combine like terms: 369 + -369 = 0 -177 + 56x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -44.25 + 14x + x2 = 0 Move the constant term to the right: Add '44.25' to each side of the equation. -44.25 + 14x + 44.25 + x2 = 0 + 44.25 Reorder the terms: -44.25 + 44.25 + 14x + x2 = 0 + 44.25 Combine like terms: -44.25 + 44.25 = 0.00 0.00 + 14x + x2 = 0 + 44.25 14x + x2 = 0 + 44.25 Combine like terms: 0 + 44.25 = 44.25 14x + x2 = 44.25 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 44.25 + 49 Reorder the terms: 49 + 14x + x2 = 44.25 + 49 Combine like terms: 44.25 + 49 = 93.25 49 + 14x + x2 = 93.25 Factor a perfect square on the left side: (x + 7)(x + 7) = 93.25 Calculate the square root of the right side: 9.656603958 Break this problem into two subproblems by setting (x + 7) equal to 9.656603958 and -9.656603958.Subproblem 1
x + 7 = 9.656603958 Simplifying x + 7 = 9.656603958 Reorder the terms: 7 + x = 9.656603958 Solving 7 + x = 9.656603958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 9.656603958 + -7 Combine like terms: 7 + -7 = 0 0 + x = 9.656603958 + -7 x = 9.656603958 + -7 Combine like terms: 9.656603958 + -7 = 2.656603958 x = 2.656603958 Simplifying x = 2.656603958Subproblem 2
x + 7 = -9.656603958 Simplifying x + 7 = -9.656603958 Reorder the terms: 7 + x = -9.656603958 Solving 7 + x = -9.656603958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -9.656603958 + -7 Combine like terms: 7 + -7 = 0 0 + x = -9.656603958 + -7 x = -9.656603958 + -7 Combine like terms: -9.656603958 + -7 = -16.656603958 x = -16.656603958 Simplifying x = -16.656603958Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.656603958, -16.656603958}
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