4x^2-19x+6=0

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Solution for 4x^2-19x+6=0 equation:


Simplifying
4x2 + -19x + 6 = 0

Reorder the terms:
6 + -19x + 4x2 = 0

Solving
6 + -19x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
1.5 + -4.75x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -4.75x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -4.75x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -4.75x + x2 = 0 + -1.5
-4.75x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-4.75x + x2 = -1.5

The x term is -4.75x.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75x + 5.640625 + x2 = -1.5 + 5.640625

Reorder the terms:
5.640625 + -4.75x + x2 = -1.5 + 5.640625

Combine like terms: -1.5 + 5.640625 = 4.140625
5.640625 + -4.75x + x2 = 4.140625

Factor a perfect square on the left side:
(x + -2.375)(x + -2.375) = 4.140625

Calculate the square root of the right side: 2.034852575

Break this problem into two subproblems by setting 
(x + -2.375) equal to 2.034852575 and -2.034852575.

Subproblem 1

x + -2.375 = 2.034852575 Simplifying x + -2.375 = 2.034852575 Reorder the terms: -2.375 + x = 2.034852575 Solving -2.375 + x = 2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 2.034852575 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 2.034852575 + 2.375 x = 2.034852575 + 2.375 Combine like terms: 2.034852575 + 2.375 = 4.409852575 x = 4.409852575 Simplifying x = 4.409852575

Subproblem 2

x + -2.375 = -2.034852575 Simplifying x + -2.375 = -2.034852575 Reorder the terms: -2.375 + x = -2.034852575 Solving -2.375 + x = -2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -2.034852575 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -2.034852575 + 2.375 x = -2.034852575 + 2.375 Combine like terms: -2.034852575 + 2.375 = 0.340147425 x = 0.340147425 Simplifying x = 0.340147425

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.409852575, 0.340147425}

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