2x^2+-23x+4=0

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Solution for 2x^2+-23x+4=0 equation:


Simplifying
2x2 + -23x + 4 = 0

Reorder the terms:
4 + -23x + 2x2 = 0

Solving
4 + -23x + 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 + -11.5x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -11.5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -11.5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -11.5x + x2 = 0 + -2
-11.5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-11.5x + x2 = -2

The x term is -11.5x.  Take half its coefficient (-5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
-11.5x + 33.0625 + x2 = -2 + 33.0625

Reorder the terms:
33.0625 + -11.5x + x2 = -2 + 33.0625

Combine like terms: -2 + 33.0625 = 31.0625
33.0625 + -11.5x + x2 = 31.0625

Factor a perfect square on the left side:
(x + -5.75)(x + -5.75) = 31.0625

Calculate the square root of the right side: 5.573374202

Break this problem into two subproblems by setting 
(x + -5.75) equal to 5.573374202 and -5.573374202.

Subproblem 1

x + -5.75 = 5.573374202 Simplifying x + -5.75 = 5.573374202 Reorder the terms: -5.75 + x = 5.573374202 Solving -5.75 + x = 5.573374202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 5.573374202 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 5.573374202 + 5.75 x = 5.573374202 + 5.75 Combine like terms: 5.573374202 + 5.75 = 11.323374202 x = 11.323374202 Simplifying x = 11.323374202

Subproblem 2

x + -5.75 = -5.573374202 Simplifying x + -5.75 = -5.573374202 Reorder the terms: -5.75 + x = -5.573374202 Solving -5.75 + x = -5.573374202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -5.573374202 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -5.573374202 + 5.75 x = -5.573374202 + 5.75 Combine like terms: -5.573374202 + 5.75 = 0.176625798 x = 0.176625798 Simplifying x = 0.176625798

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.323374202, 0.176625798}

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