2x^2-19x+4=0

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


Simplifying
2x2 + -19x + 4 = 0

Reorder the terms:
4 + -19x + 2x2 = 0

Solving
4 + -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'.
2 + -9.5x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -9.5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -9.5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9.5x + x2 = 0 + -2
-9.5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-9.5x + x2 = -2

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 = -2 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = -2 + 22.5625

Combine like terms: -2 + 22.5625 = 20.5625
22.5625 + -9.5x + x2 = 20.5625

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(x + -4.75) equal to 4.534589287 and -4.534589287.

Subproblem 1

x + -4.75 = 4.534589287 Simplifying x + -4.75 = 4.534589287 Reorder the terms: -4.75 + x = 4.534589287 Solving -4.75 + x = 4.534589287 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 = 4.534589287 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 4.534589287 + 4.75 x = 4.534589287 + 4.75 Combine like terms: 4.534589287 + 4.75 = 9.284589287 x = 9.284589287 Simplifying x = 9.284589287

Subproblem 2

x + -4.75 = -4.534589287 Simplifying x + -4.75 = -4.534589287 Reorder the terms: -4.75 + x = -4.534589287 Solving -4.75 + x = -4.534589287 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 = -4.534589287 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -4.534589287 + 4.75 x = -4.534589287 + 4.75 Combine like terms: -4.534589287 + 4.75 = 0.215410713 x = 0.215410713 Simplifying x = 0.215410713

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.284589287, 0.215410713}

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