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Simplifying (181520 + -1x) * 20670(229900 + -1x) = 3000 Reorder the terms for easier multiplication: 20670(181520 + -1x)(229900 + -1x) = 3000 Multiply (181520 + -1x) * (229900 + -1x) 20670(181520(229900 + -1x) + -1x * (229900 + -1x)) = 3000 20670((229900 * 181520 + -1x * 181520) + -1x * (229900 + -1x)) = 3000 20670((41731448000 + -181520x) + -1x * (229900 + -1x)) = 3000 20670(41731448000 + -181520x + (229900 * -1x + -1x * -1x)) = 3000 20670(41731448000 + -181520x + (-229900x + 1x2)) = 3000 Combine like terms: -181520x + -229900x = -411420x 20670(41731448000 + -411420x + 1x2) = 3000 (41731448000 * 20670 + -411420x * 20670 + 1x2 * 20670) = 3000 (862589030200000 + -8504051400x + 20670x2) = 3000 Solving 862589030200000 + -8504051400x + 20670x2 = 3000 Solving for variable 'x'. Reorder the terms: 862589030200000 + -3000 + -8504051400x + 20670x2 = 3000 + -3000 Combine like terms: 862589030200000 + -3000 = 862589030197000 862589030197000 + -8504051400x + 20670x2 = 3000 + -3000 Combine like terms: 3000 + -3000 = 0 862589030197000 + -8504051400x + 20670x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(86258903020000 + -850405140x + 2067x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(86258903020000 + -850405140x + 2067x2)' equal to zero and attempt to solve: Simplifying 86258903020000 + -850405140x + 2067x2 = 0 Solving 86258903020000 + -850405140x + 2067x2 = 0 Begin completing the square. Divide all terms by 2067 the coefficient of the squared term: Divide each side by '2067'. 41731448000 + -411420x + x2 = 0 Move the constant term to the right: Add '-41731448000' to each side of the equation. 41731448000 + -411420x + -41731448000 + x2 = 0 + -41731448000 Reorder the terms: 41731448000 + -41731448000 + -411420x + x2 = 0 + -41731448000 Combine like terms: 41731448000 + -41731448000 = 0 0 + -411420x + x2 = 0 + -41731448000 -411420x + x2 = 0 + -41731448000 Combine like terms: 0 + -41731448000 = -41731448000 -411420x + x2 = -41731448000 The x term is -411420x. Take half its coefficient (-205710). Square it (42316604100) and add it to both sides. Add '42316604100' to each side of the equation. -411420x + 42316604100 + x2 = -41731448000 + 42316604100 Reorder the terms: 42316604100 + -411420x + x2 = -41731448000 + 42316604100 Combine like terms: -41731448000 + 42316604100 = 585156100 42316604100 + -411420x + x2 = 585156100 Factor a perfect square on the left side: (x + -205710)(x + -205710) = 585156100 Calculate the square root of the right side: 24190 Break this problem into two subproblems by setting (x + -205710) equal to 24190 and -24190.Subproblem 1
x + -205710 = 24190 Simplifying x + -205710 = 24190 Reorder the terms: -205710 + x = 24190 Solving -205710 + x = 24190 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '205710' to each side of the equation. -205710 + 205710 + x = 24190 + 205710 Combine like terms: -205710 + 205710 = 0 0 + x = 24190 + 205710 x = 24190 + 205710 Combine like terms: 24190 + 205710 = 229900 x = 229900 Simplifying x = 229900Subproblem 2
x + -205710 = -24190 Simplifying x + -205710 = -24190 Reorder the terms: -205710 + x = -24190 Solving -205710 + x = -24190 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '205710' to each side of the equation. -205710 + 205710 + x = -24190 + 205710 Combine like terms: -205710 + 205710 = 0 0 + x = -24190 + 205710 x = -24190 + 205710 Combine like terms: -24190 + 205710 = 181520 x = 181520 Simplifying x = 181520Solution
The solution to the problem is based on the solutions from the subproblems. x = {229900, 181520}Solution
x = {229900, 181520}
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