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Simplifying 18x2 + -62x + 46 = 0 Reorder the terms: 46 + -62x + 18x2 = 0 Solving 46 + -62x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(23 + -31x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(23 + -31x + 9x2)' equal to zero and attempt to solve: Simplifying 23 + -31x + 9x2 = 0 Solving 23 + -31x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2.555555556 + -3.444444444x + x2 = 0 Move the constant term to the right: Add '-2.555555556' to each side of the equation. 2.555555556 + -3.444444444x + -2.555555556 + x2 = 0 + -2.555555556 Reorder the terms: 2.555555556 + -2.555555556 + -3.444444444x + x2 = 0 + -2.555555556 Combine like terms: 2.555555556 + -2.555555556 = 0.000000000 0.000000000 + -3.444444444x + x2 = 0 + -2.555555556 -3.444444444x + x2 = 0 + -2.555555556 Combine like terms: 0 + -2.555555556 = -2.555555556 -3.444444444x + x2 = -2.555555556 The x term is -3.444444444x. Take half its coefficient (-1.722222222). Square it (2.966049382) and add it to both sides. Add '2.966049382' to each side of the equation. -3.444444444x + 2.966049382 + x2 = -2.555555556 + 2.966049382 Reorder the terms: 2.966049382 + -3.444444444x + x2 = -2.555555556 + 2.966049382 Combine like terms: -2.555555556 + 2.966049382 = 0.410493826 2.966049382 + -3.444444444x + x2 = 0.410493826 Factor a perfect square on the left side: (x + -1.722222222)(x + -1.722222222) = 0.410493826 Calculate the square root of the right side: 0.640697921 Break this problem into two subproblems by setting (x + -1.722222222) equal to 0.640697921 and -0.640697921.Subproblem 1
x + -1.722222222 = 0.640697921 Simplifying x + -1.722222222 = 0.640697921 Reorder the terms: -1.722222222 + x = 0.640697921 Solving -1.722222222 + x = 0.640697921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.722222222' to each side of the equation. -1.722222222 + 1.722222222 + x = 0.640697921 + 1.722222222 Combine like terms: -1.722222222 + 1.722222222 = 0.000000000 0.000000000 + x = 0.640697921 + 1.722222222 x = 0.640697921 + 1.722222222 Combine like terms: 0.640697921 + 1.722222222 = 2.362920143 x = 2.362920143 Simplifying x = 2.362920143Subproblem 2
x + -1.722222222 = -0.640697921 Simplifying x + -1.722222222 = -0.640697921 Reorder the terms: -1.722222222 + x = -0.640697921 Solving -1.722222222 + x = -0.640697921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.722222222' to each side of the equation. -1.722222222 + 1.722222222 + x = -0.640697921 + 1.722222222 Combine like terms: -1.722222222 + 1.722222222 = 0.000000000 0.000000000 + x = -0.640697921 + 1.722222222 x = -0.640697921 + 1.722222222 Combine like terms: -0.640697921 + 1.722222222 = 1.081524301 x = 1.081524301 Simplifying x = 1.081524301Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.362920143, 1.081524301}Solution
x = {2.362920143, 1.081524301}
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