(2x^2)-7x+4=0

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Solution for (2x^2)-7x+4=0 equation:


Simplifying
(2x2) + -7x + 4 = 0

Reorder the terms:
4 + -7x + (2x2) = 0

Solving
4 + -7x + (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 + -3.5x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -3.5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -3.5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3.5x + x2 = 0 + -2
-3.5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3.5x + x2 = -2

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -2 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -2 + 3.0625

Combine like terms: -2 + 3.0625 = 1.0625
3.0625 + -3.5x + x2 = 1.0625

Factor a perfect square on the left side:
((x) + -1.75)((x) + -1.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
((x) + -1.75) equal to 1.030776406 and -1.030776406.

Subproblem 1

(x) + -1.75 = 1.030776406 Simplifying (x) + -1.75 = 1.030776406 x + -1.75 = 1.030776406 Reorder the terms: -1.75 + x = 1.030776406 Solving -1.75 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.030776406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.030776406 + 1.75 x = 1.030776406 + 1.75 Combine like terms: 1.030776406 + 1.75 = 2.780776406 x = 2.780776406 Simplifying x = 2.780776406

Subproblem 2

(x) + -1.75 = -1.030776406 Simplifying (x) + -1.75 = -1.030776406 x + -1.75 = -1.030776406 Reorder the terms: -1.75 + x = -1.030776406 Solving -1.75 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.030776406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.030776406 + 1.75 x = -1.030776406 + 1.75 Combine like terms: -1.030776406 + 1.75 = 0.719223594 x = 0.719223594 Simplifying x = 0.719223594

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.780776406, 0.719223594}

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