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Simplifying 0 = 2(x2 + -252x + 8640) Reorder the terms: 0 = 2(8640 + -252x + x2) 0 = (8640 * 2 + -252x * 2 + x2 * 2) 0 = (17280 + -504x + 2x2) Solving 0 = 17280 + -504x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -17280 = -17280 -17280 + 504x + -2x2 = 17280 + -504x + 2x2 + -17280 + 504x + -2x2 Reorder the terms: -17280 + 504x + -2x2 = 17280 + -17280 + -504x + 504x + 2x2 + -2x2 Combine like terms: 17280 + -17280 = 0 -17280 + 504x + -2x2 = 0 + -504x + 504x + 2x2 + -2x2 -17280 + 504x + -2x2 = -504x + 504x + 2x2 + -2x2 Combine like terms: -504x + 504x = 0 -17280 + 504x + -2x2 = 0 + 2x2 + -2x2 -17280 + 504x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -17280 + 504x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8640 + 252x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8640 + 252x + -1x2)' equal to zero and attempt to solve: Simplifying -8640 + 252x + -1x2 = 0 Solving -8640 + 252x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8640 + -252x + x2 = 0 Move the constant term to the right: Add '-8640' to each side of the equation. 8640 + -252x + -8640 + x2 = 0 + -8640 Reorder the terms: 8640 + -8640 + -252x + x2 = 0 + -8640 Combine like terms: 8640 + -8640 = 0 0 + -252x + x2 = 0 + -8640 -252x + x2 = 0 + -8640 Combine like terms: 0 + -8640 = -8640 -252x + x2 = -8640 The x term is -252x. Take half its coefficient (-126). Square it (15876) and add it to both sides. Add '15876' to each side of the equation. -252x + 15876 + x2 = -8640 + 15876 Reorder the terms: 15876 + -252x + x2 = -8640 + 15876 Combine like terms: -8640 + 15876 = 7236 15876 + -252x + x2 = 7236 Factor a perfect square on the left side: (x + -126)(x + -126) = 7236 Calculate the square root of the right side: 85.064681273 Break this problem into two subproblems by setting (x + -126) equal to 85.064681273 and -85.064681273.Subproblem 1
x + -126 = 85.064681273 Simplifying x + -126 = 85.064681273 Reorder the terms: -126 + x = 85.064681273 Solving -126 + x = 85.064681273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '126' to each side of the equation. -126 + 126 + x = 85.064681273 + 126 Combine like terms: -126 + 126 = 0 0 + x = 85.064681273 + 126 x = 85.064681273 + 126 Combine like terms: 85.064681273 + 126 = 211.064681273 x = 211.064681273 Simplifying x = 211.064681273Subproblem 2
x + -126 = -85.064681273 Simplifying x + -126 = -85.064681273 Reorder the terms: -126 + x = -85.064681273 Solving -126 + x = -85.064681273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '126' to each side of the equation. -126 + 126 + x = -85.064681273 + 126 Combine like terms: -126 + 126 = 0 0 + x = -85.064681273 + 126 x = -85.064681273 + 126 Combine like terms: -85.064681273 + 126 = 40.935318727 x = 40.935318727 Simplifying x = 40.935318727Solution
The solution to the problem is based on the solutions from the subproblems. x = {211.064681273, 40.935318727}Solution
x = {211.064681273, 40.935318727}
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