28x^2-54x+5=0

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Solution for 28x^2-54x+5=0 equation:


Simplifying
28x2 + -54x + 5 = 0

Reorder the terms:
5 + -54x + 28x2 = 0

Solving
5 + -54x + 28x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
28 the coefficient of the squared term: 

Divide each side by '28'.
0.1785714286 + -1.928571429x + x2 = 0

Move the constant term to the right:

Add '-0.1785714286' to each side of the equation.
0.1785714286 + -1.928571429x + -0.1785714286 + x2 = 0 + -0.1785714286

Reorder the terms:
0.1785714286 + -0.1785714286 + -1.928571429x + x2 = 0 + -0.1785714286

Combine like terms: 0.1785714286 + -0.1785714286 = 0.0000000000
0.0000000000 + -1.928571429x + x2 = 0 + -0.1785714286
-1.928571429x + x2 = 0 + -0.1785714286

Combine like terms: 0 + -0.1785714286 = -0.1785714286
-1.928571429x + x2 = -0.1785714286

The x term is -1.928571429x.  Take half its coefficient (-0.9642857145).
Square it (0.9298469392) and add it to both sides.

Add '0.9298469392' to each side of the equation.
-1.928571429x + 0.9298469392 + x2 = -0.1785714286 + 0.9298469392

Reorder the terms:
0.9298469392 + -1.928571429x + x2 = -0.1785714286 + 0.9298469392

Combine like terms: -0.1785714286 + 0.9298469392 = 0.7512755106
0.9298469392 + -1.928571429x + x2 = 0.7512755106

Factor a perfect square on the left side:
(x + -0.9642857145)(x + -0.9642857145) = 0.7512755106

Calculate the square root of the right side: 0.866761507

Break this problem into two subproblems by setting 
(x + -0.9642857145) equal to 0.866761507 and -0.866761507.

Subproblem 1

x + -0.9642857145 = 0.866761507 Simplifying x + -0.9642857145 = 0.866761507 Reorder the terms: -0.9642857145 + x = 0.866761507 Solving -0.9642857145 + x = 0.866761507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9642857145' to each side of the equation. -0.9642857145 + 0.9642857145 + x = 0.866761507 + 0.9642857145 Combine like terms: -0.9642857145 + 0.9642857145 = 0.0000000000 0.0000000000 + x = 0.866761507 + 0.9642857145 x = 0.866761507 + 0.9642857145 Combine like terms: 0.866761507 + 0.9642857145 = 1.8310472215 x = 1.8310472215 Simplifying x = 1.8310472215

Subproblem 2

x + -0.9642857145 = -0.866761507 Simplifying x + -0.9642857145 = -0.866761507 Reorder the terms: -0.9642857145 + x = -0.866761507 Solving -0.9642857145 + x = -0.866761507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9642857145' to each side of the equation. -0.9642857145 + 0.9642857145 + x = -0.866761507 + 0.9642857145 Combine like terms: -0.9642857145 + 0.9642857145 = 0.0000000000 0.0000000000 + x = -0.866761507 + 0.9642857145 x = -0.866761507 + 0.9642857145 Combine like terms: -0.866761507 + 0.9642857145 = 0.0975242075 x = 0.0975242075 Simplifying x = 0.0975242075

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.8310472215, 0.0975242075}

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