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Simplifying 1011x + 1071x * x = 680616 Multiply x * x 1011x + 1071x2 = 680616 Solving 1011x + 1071x2 = 680616 Solving for variable 'x'. Reorder the terms: -680616 + 1011x + 1071x2 = 680616 + -680616 Combine like terms: 680616 + -680616 = 0 -680616 + 1011x + 1071x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-226872 + 337x + 357x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-226872 + 337x + 357x2)' equal to zero and attempt to solve: Simplifying -226872 + 337x + 357x2 = 0 Solving -226872 + 337x + 357x2 = 0 Begin completing the square. Divide all terms by 357 the coefficient of the squared term: Divide each side by '357'. -635.4957983 + 0.943977591x + x2 = 0 Move the constant term to the right: Add '635.4957983' to each side of the equation. -635.4957983 + 0.943977591x + 635.4957983 + x2 = 0 + 635.4957983 Reorder the terms: -635.4957983 + 635.4957983 + 0.943977591x + x2 = 0 + 635.4957983 Combine like terms: -635.4957983 + 635.4957983 = 0.0000000 0.0000000 + 0.943977591x + x2 = 0 + 635.4957983 0.943977591x + x2 = 0 + 635.4957983 Combine like terms: 0 + 635.4957983 = 635.4957983 0.943977591x + x2 = 635.4957983 The x term is 0.943977591x. Take half its coefficient (0.4719887955). Square it (0.2227734231) and add it to both sides. Add '0.2227734231' to each side of the equation. 0.943977591x + 0.2227734231 + x2 = 635.4957983 + 0.2227734231 Reorder the terms: 0.2227734231 + 0.943977591x + x2 = 635.4957983 + 0.2227734231 Combine like terms: 635.4957983 + 0.2227734231 = 635.7185717231 0.2227734231 + 0.943977591x + x2 = 635.7185717231 Factor a perfect square on the left side: (x + 0.4719887955)(x + 0.4719887955) = 635.7185717231 Calculate the square root of the right side: 25.21346013 Break this problem into two subproblems by setting (x + 0.4719887955) equal to 25.21346013 and -25.21346013.Subproblem 1
x + 0.4719887955 = 25.21346013 Simplifying x + 0.4719887955 = 25.21346013 Reorder the terms: 0.4719887955 + x = 25.21346013 Solving 0.4719887955 + x = 25.21346013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4719887955' to each side of the equation. 0.4719887955 + -0.4719887955 + x = 25.21346013 + -0.4719887955 Combine like terms: 0.4719887955 + -0.4719887955 = 0.0000000000 0.0000000000 + x = 25.21346013 + -0.4719887955 x = 25.21346013 + -0.4719887955 Combine like terms: 25.21346013 + -0.4719887955 = 24.7414713345 x = 24.7414713345 Simplifying x = 24.7414713345Subproblem 2
x + 0.4719887955 = -25.21346013 Simplifying x + 0.4719887955 = -25.21346013 Reorder the terms: 0.4719887955 + x = -25.21346013 Solving 0.4719887955 + x = -25.21346013 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4719887955' to each side of the equation. 0.4719887955 + -0.4719887955 + x = -25.21346013 + -0.4719887955 Combine like terms: 0.4719887955 + -0.4719887955 = 0.0000000000 0.0000000000 + x = -25.21346013 + -0.4719887955 x = -25.21346013 + -0.4719887955 Combine like terms: -25.21346013 + -0.4719887955 = -25.6854489255 x = -25.6854489255 Simplifying x = -25.6854489255Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.7414713345, -25.6854489255}Solution
x = {24.7414713345, -25.6854489255}
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