46x^2-108x+34=0

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Solution for 46x^2-108x+34=0 equation:


Simplifying
46x2 + -108x + 34 = 0

Reorder the terms:
34 + -108x + 46x2 = 0

Solving
34 + -108x + 46x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + -54x + 23x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(17 + -54x + 23x2)' equal to zero and attempt to solve: Simplifying 17 + -54x + 23x2 = 0 Solving 17 + -54x + 23x2 = 0 Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. 0.7391304348 + -2.347826087x + x2 = 0 Move the constant term to the right: Add '-0.7391304348' to each side of the equation. 0.7391304348 + -2.347826087x + -0.7391304348 + x2 = 0 + -0.7391304348 Reorder the terms: 0.7391304348 + -0.7391304348 + -2.347826087x + x2 = 0 + -0.7391304348 Combine like terms: 0.7391304348 + -0.7391304348 = 0.0000000000 0.0000000000 + -2.347826087x + x2 = 0 + -0.7391304348 -2.347826087x + x2 = 0 + -0.7391304348 Combine like terms: 0 + -0.7391304348 = -0.7391304348 -2.347826087x + x2 = -0.7391304348 The x term is -2.347826087x. Take half its coefficient (-1.173913044). Square it (1.378071835) and add it to both sides. Add '1.378071835' to each side of the equation. -2.347826087x + 1.378071835 + x2 = -0.7391304348 + 1.378071835 Reorder the terms: 1.378071835 + -2.347826087x + x2 = -0.7391304348 + 1.378071835 Combine like terms: -0.7391304348 + 1.378071835 = 0.6389414002 1.378071835 + -2.347826087x + x2 = 0.6389414002 Factor a perfect square on the left side: (x + -1.173913044)(x + -1.173913044) = 0.6389414002 Calculate the square root of the right side: 0.799338101 Break this problem into two subproblems by setting (x + -1.173913044) equal to 0.799338101 and -0.799338101.

Subproblem 1

x + -1.173913044 = 0.799338101 Simplifying x + -1.173913044 = 0.799338101 Reorder the terms: -1.173913044 + x = 0.799338101 Solving -1.173913044 + x = 0.799338101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.173913044' to each side of the equation. -1.173913044 + 1.173913044 + x = 0.799338101 + 1.173913044 Combine like terms: -1.173913044 + 1.173913044 = 0.000000000 0.000000000 + x = 0.799338101 + 1.173913044 x = 0.799338101 + 1.173913044 Combine like terms: 0.799338101 + 1.173913044 = 1.973251145 x = 1.973251145 Simplifying x = 1.973251145

Subproblem 2

x + -1.173913044 = -0.799338101 Simplifying x + -1.173913044 = -0.799338101 Reorder the terms: -1.173913044 + x = -0.799338101 Solving -1.173913044 + x = -0.799338101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.173913044' to each side of the equation. -1.173913044 + 1.173913044 + x = -0.799338101 + 1.173913044 Combine like terms: -1.173913044 + 1.173913044 = 0.000000000 0.000000000 + x = -0.799338101 + 1.173913044 x = -0.799338101 + 1.173913044 Combine like terms: -0.799338101 + 1.173913044 = 0.374574943 x = 0.374574943 Simplifying x = 0.374574943

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.973251145, 0.374574943}

Solution

x = {1.973251145, 0.374574943}

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