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Simplifying (20 + 2x)(10x + 2x) = 1064 Combine like terms: 10x + 2x = 12x (20 + 2x)(12x) = 1064 Remove parenthesis around (12x) (20 + 2x) * 12x = 1064 Reorder the terms for easier multiplication: 12x(20 + 2x) = 1064 (20 * 12x + 2x * 12x) = 1064 (240x + 24x2) = 1064 Solving 240x + 24x2 = 1064 Solving for variable 'x'. Reorder the terms: -1064 + 240x + 24x2 = 1064 + -1064 Combine like terms: 1064 + -1064 = 0 -1064 + 240x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-133 + 30x + 3x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-133 + 30x + 3x2)' equal to zero and attempt to solve: Simplifying -133 + 30x + 3x2 = 0 Solving -133 + 30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -44.33333333 + 10x + x2 = 0 Move the constant term to the right: Add '44.33333333' to each side of the equation. -44.33333333 + 10x + 44.33333333 + x2 = 0 + 44.33333333 Reorder the terms: -44.33333333 + 44.33333333 + 10x + x2 = 0 + 44.33333333 Combine like terms: -44.33333333 + 44.33333333 = 0.00000000 0.00000000 + 10x + x2 = 0 + 44.33333333 10x + x2 = 0 + 44.33333333 Combine like terms: 0 + 44.33333333 = 44.33333333 10x + x2 = 44.33333333 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 44.33333333 + 25 Reorder the terms: 25 + 10x + x2 = 44.33333333 + 25 Combine like terms: 44.33333333 + 25 = 69.33333333 25 + 10x + x2 = 69.33333333 Factor a perfect square on the left side: (x + 5)(x + 5) = 69.33333333 Calculate the square root of the right side: 8.326663998 Break this problem into two subproblems by setting (x + 5) equal to 8.326663998 and -8.326663998.Subproblem 1
x + 5 = 8.326663998 Simplifying x + 5 = 8.326663998 Reorder the terms: 5 + x = 8.326663998 Solving 5 + x = 8.326663998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 8.326663998 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.326663998 + -5 x = 8.326663998 + -5 Combine like terms: 8.326663998 + -5 = 3.326663998 x = 3.326663998 Simplifying x = 3.326663998Subproblem 2
x + 5 = -8.326663998 Simplifying x + 5 = -8.326663998 Reorder the terms: 5 + x = -8.326663998 Solving 5 + x = -8.326663998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -8.326663998 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.326663998 + -5 x = -8.326663998 + -5 Combine like terms: -8.326663998 + -5 = -13.326663998 x = -13.326663998 Simplifying x = -13.326663998Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.326663998, -13.326663998}Solution
x = {3.326663998, -13.326663998}
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