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Simplifying (12x + 2x)(16 + 2x) = 396 Combine like terms: 12x + 2x = 14x (14x)(16 + 2x) = 396 Remove parenthesis around (14x) 14x(16 + 2x) = 396 (16 * 14x + 2x * 14x) = 396 (224x + 28x2) = 396 Solving 224x + 28x2 = 396 Solving for variable 'x'. Reorder the terms: -396 + 224x + 28x2 = 396 + -396 Combine like terms: 396 + -396 = 0 -396 + 224x + 28x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-99 + 56x + 7x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-99 + 56x + 7x2)' equal to zero and attempt to solve: Simplifying -99 + 56x + 7x2 = 0 Solving -99 + 56x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -14.14285714 + 8x + x2 = 0 Move the constant term to the right: Add '14.14285714' to each side of the equation. -14.14285714 + 8x + 14.14285714 + x2 = 0 + 14.14285714 Reorder the terms: -14.14285714 + 14.14285714 + 8x + x2 = 0 + 14.14285714 Combine like terms: -14.14285714 + 14.14285714 = 0.00000000 0.00000000 + 8x + x2 = 0 + 14.14285714 8x + x2 = 0 + 14.14285714 Combine like terms: 0 + 14.14285714 = 14.14285714 8x + x2 = 14.14285714 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 14.14285714 + 16 Reorder the terms: 16 + 8x + x2 = 14.14285714 + 16 Combine like terms: 14.14285714 + 16 = 30.14285714 16 + 8x + x2 = 30.14285714 Factor a perfect square on the left side: (x + 4)(x + 4) = 30.14285714 Calculate the square root of the right side: 5.4902511 Break this problem into two subproblems by setting (x + 4) equal to 5.4902511 and -5.4902511.Subproblem 1
x + 4 = 5.4902511 Simplifying x + 4 = 5.4902511 Reorder the terms: 4 + x = 5.4902511 Solving 4 + x = 5.4902511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.4902511 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.4902511 + -4 x = 5.4902511 + -4 Combine like terms: 5.4902511 + -4 = 1.4902511 x = 1.4902511 Simplifying x = 1.4902511Subproblem 2
x + 4 = -5.4902511 Simplifying x + 4 = -5.4902511 Reorder the terms: 4 + x = -5.4902511 Solving 4 + x = -5.4902511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.4902511 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.4902511 + -4 x = -5.4902511 + -4 Combine like terms: -5.4902511 + -4 = -9.4902511 x = -9.4902511 Simplifying x = -9.4902511Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4902511, -9.4902511}Solution
x = {1.4902511, -9.4902511}
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