2x^2-19x+6=0

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


Simplifying
2x2 + -19x + 6 = 0

Reorder the terms:
6 + -19x + 2x2 = 0

Solving
6 + -19x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
3 + -9.5x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -9.5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -9.5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -9.5x + x2 = 0 + -3
-9.5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-9.5x + x2 = -3

The x term is -9.5x.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5x + 22.5625 + x2 = -3 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = -3 + 22.5625

Combine like terms: -3 + 22.5625 = 19.5625
22.5625 + -9.5x + x2 = 19.5625

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 19.5625

Calculate the square root of the right side: 4.422951503

Break this problem into two subproblems by setting 
(x + -4.75) equal to 4.422951503 and -4.422951503.

Subproblem 1

x + -4.75 = 4.422951503 Simplifying x + -4.75 = 4.422951503 Reorder the terms: -4.75 + x = 4.422951503 Solving -4.75 + x = 4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 4.422951503 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 4.422951503 + 4.75 x = 4.422951503 + 4.75 Combine like terms: 4.422951503 + 4.75 = 9.172951503 x = 9.172951503 Simplifying x = 9.172951503

Subproblem 2

x + -4.75 = -4.422951503 Simplifying x + -4.75 = -4.422951503 Reorder the terms: -4.75 + x = -4.422951503 Solving -4.75 + x = -4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -4.422951503 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -4.422951503 + 4.75 x = -4.422951503 + 4.75 Combine like terms: -4.422951503 + 4.75 = 0.327048497 x = 0.327048497 Simplifying x = 0.327048497

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.172951503, 0.327048497}

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