(4x^2)-21x+4=0

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


Simplifying
(4x2) + -21x + 4 = 0

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

Solving
4 + -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'.
1 + -5.25x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -5.25x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -5.25x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5.25x + x2 = 0 + -1
-5.25x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-5.25x + x2 = -1

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 = -1 + 6.890625

Reorder the terms:
6.890625 + -5.25x + x2 = -1 + 6.890625

Combine like terms: -1 + 6.890625 = 5.890625
6.890625 + -5.25x + x2 = 5.890625

Factor a perfect square on the left side:
((x) + -2.625)((x) + -2.625) = 5.890625

Calculate the square root of the right side: 2.42706098

Break this problem into two subproblems by setting 
((x) + -2.625) equal to 2.42706098 and -2.42706098.

Subproblem 1

(x) + -2.625 = 2.42706098 Simplifying (x) + -2.625 = 2.42706098 x + -2.625 = 2.42706098 Reorder the terms: -2.625 + x = 2.42706098 Solving -2.625 + x = 2.42706098 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 = 2.42706098 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 2.42706098 + 2.625 x = 2.42706098 + 2.625 Combine like terms: 2.42706098 + 2.625 = 5.05206098 x = 5.05206098 Simplifying x = 5.05206098

Subproblem 2

(x) + -2.625 = -2.42706098 Simplifying (x) + -2.625 = -2.42706098 x + -2.625 = -2.42706098 Reorder the terms: -2.625 + x = -2.42706098 Solving -2.625 + x = -2.42706098 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 = -2.42706098 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -2.42706098 + 2.625 x = -2.42706098 + 2.625 Combine like terms: -2.42706098 + 2.625 = 0.19793902 x = 0.19793902 Simplifying x = 0.19793902

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.05206098, 0.19793902}

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