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Simplifying (16x + 60)(8x) = 180 Reorder the terms: (60 + 16x)(8x) = 180 Remove parenthesis around (8x) (60 + 16x) * 8x = 180 Reorder the terms for easier multiplication: 8x(60 + 16x) = 180 (60 * 8x + 16x * 8x) = 180 (480x + 128x2) = 180 Solving 480x + 128x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 480x + 128x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 480x + 128x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + 120x + 32x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-45 + 120x + 32x2)' equal to zero and attempt to solve: Simplifying -45 + 120x + 32x2 = 0 Solving -45 + 120x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -1.40625 + 3.75x + x2 = 0 Move the constant term to the right: Add '1.40625' to each side of the equation. -1.40625 + 3.75x + 1.40625 + x2 = 0 + 1.40625 Reorder the terms: -1.40625 + 1.40625 + 3.75x + x2 = 0 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + 3.75x + x2 = 0 + 1.40625 3.75x + x2 = 0 + 1.40625 Combine like terms: 0 + 1.40625 = 1.40625 3.75x + x2 = 1.40625 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 1.40625 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 1.40625 + 3.515625 Combine like terms: 1.40625 + 3.515625 = 4.921875 3.515625 + 3.75x + x2 = 4.921875 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 4.921875 Calculate the square root of the right side: 2.218529919 Break this problem into two subproblems by setting (x + 1.875) equal to 2.218529919 and -2.218529919.Subproblem 1
x + 1.875 = 2.218529919 Simplifying x + 1.875 = 2.218529919 Reorder the terms: 1.875 + x = 2.218529919 Solving 1.875 + x = 2.218529919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 2.218529919 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 2.218529919 + -1.875 x = 2.218529919 + -1.875 Combine like terms: 2.218529919 + -1.875 = 0.343529919 x = 0.343529919 Simplifying x = 0.343529919Subproblem 2
x + 1.875 = -2.218529919 Simplifying x + 1.875 = -2.218529919 Reorder the terms: 1.875 + x = -2.218529919 Solving 1.875 + x = -2.218529919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -2.218529919 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -2.218529919 + -1.875 x = -2.218529919 + -1.875 Combine like terms: -2.218529919 + -1.875 = -4.093529919 x = -4.093529919 Simplifying x = -4.093529919Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.343529919, -4.093529919}Solution
x = {0.343529919, -4.093529919}
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