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Simplifying 3456x + -789 = 678x * x Reorder the terms: -789 + 3456x = 678x * x Multiply x * x -789 + 3456x = 678x2 Solving -789 + 3456x = 678x2 Solving for variable 'x'. Combine like terms: 678x2 + -678x2 = 0 -789 + 3456x + -678x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-263 + 1152x + -226x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-263 + 1152x + -226x2)' equal to zero and attempt to solve: Simplifying -263 + 1152x + -226x2 = 0 Solving -263 + 1152x + -226x2 = 0 Begin completing the square. Divide all terms by -226 the coefficient of the squared term: Divide each side by '-226'. 1.163716814 + -5.097345133x + x2 = 0 Move the constant term to the right: Add '-1.163716814' to each side of the equation. 1.163716814 + -5.097345133x + -1.163716814 + x2 = 0 + -1.163716814 Reorder the terms: 1.163716814 + -1.163716814 + -5.097345133x + x2 = 0 + -1.163716814 Combine like terms: 1.163716814 + -1.163716814 = 0.000000000 0.000000000 + -5.097345133x + x2 = 0 + -1.163716814 -5.097345133x + x2 = 0 + -1.163716814 Combine like terms: 0 + -1.163716814 = -1.163716814 -5.097345133x + x2 = -1.163716814 The x term is -5.097345133x. Take half its coefficient (-2.548672567). Square it (6.495731854) and add it to both sides. Add '6.495731854' to each side of the equation. -5.097345133x + 6.495731854 + x2 = -1.163716814 + 6.495731854 Reorder the terms: 6.495731854 + -5.097345133x + x2 = -1.163716814 + 6.495731854 Combine like terms: -1.163716814 + 6.495731854 = 5.33201504 6.495731854 + -5.097345133x + x2 = 5.33201504 Factor a perfect square on the left side: (x + -2.548672567)(x + -2.548672567) = 5.33201504 Calculate the square root of the right side: 2.30911564 Break this problem into two subproblems by setting (x + -2.548672567) equal to 2.30911564 and -2.30911564.Subproblem 1
x + -2.548672567 = 2.30911564 Simplifying x + -2.548672567 = 2.30911564 Reorder the terms: -2.548672567 + x = 2.30911564 Solving -2.548672567 + x = 2.30911564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.548672567' to each side of the equation. -2.548672567 + 2.548672567 + x = 2.30911564 + 2.548672567 Combine like terms: -2.548672567 + 2.548672567 = 0.000000000 0.000000000 + x = 2.30911564 + 2.548672567 x = 2.30911564 + 2.548672567 Combine like terms: 2.30911564 + 2.548672567 = 4.857788207 x = 4.857788207 Simplifying x = 4.857788207Subproblem 2
x + -2.548672567 = -2.30911564 Simplifying x + -2.548672567 = -2.30911564 Reorder the terms: -2.548672567 + x = -2.30911564 Solving -2.548672567 + x = -2.30911564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.548672567' to each side of the equation. -2.548672567 + 2.548672567 + x = -2.30911564 + 2.548672567 Combine like terms: -2.548672567 + 2.548672567 = 0.000000000 0.000000000 + x = -2.30911564 + 2.548672567 x = -2.30911564 + 2.548672567 Combine like terms: -2.30911564 + 2.548672567 = 0.239556927 x = 0.239556927 Simplifying x = 0.239556927Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.857788207, 0.239556927}Solution
x = {4.857788207, 0.239556927}
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