4x^2-21x+2=0

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Solution for 4x^2-21x+2=0 equation: 


Simplifying
4x2 + -21x + 2 = 0

Reorder the terms:
2 + -21x + 4x2 = 0

Solving
2 + -21x + 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'.
0.5 + -5.25x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -5.25x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -5.25x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -5.25x + x2 = 0 + -0.5
-5.25x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-5.25x + x2 = -0.5

The x term is -5.25x.  Take half its coefficient (-2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
-5.25x + 6.890625 + x2 = -0.5 + 6.890625

Reorder the terms:
6.890625 + -5.25x + x2 = -0.5 + 6.890625

Combine like terms: -0.5 + 6.890625 = 6.390625
6.890625 + -5.25x + x2 = 6.390625

Factor a perfect square on the left side:
(x + -2.625)(x + -2.625) = 6.390625

Calculate the square root of the right side: 2.527968552

Break this problem into two subproblems by setting 
(x + -2.625) equal to 2.527968552 and -2.527968552.


Subproblem 1
x + -2.625 = 2.527968552

Simplifying
x + -2.625 = 2.527968552

Reorder the terms:
-2.625 + x = 2.527968552

Solving
-2.625 + x = 2.527968552

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.625' to each side of the equation.
-2.625 + 2.625 + x = 2.527968552 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + x = 2.527968552 + 2.625
x = 2.527968552 + 2.625

Combine like terms: 2.527968552 + 2.625 = 5.152968552
x = 5.152968552

Simplifying
x = 5.152968552


Subproblem 2
x + -2.625 = -2.527968552

Simplifying
x + -2.625 = -2.527968552

Reorder the terms:
-2.625 + x = -2.527968552

Solving
-2.625 + x = -2.527968552

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.625' to each side of the equation.
-2.625 + 2.625 + x = -2.527968552 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + x = -2.527968552 + 2.625
x = -2.527968552 + 2.625

Combine like terms: -2.527968552 + 2.625 = 0.097031448
x = 0.097031448

Simplifying
x = 0.097031448


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.152968552, 0.097031448}

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