2x^2-21x+4=0

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


Simplifying
2x2 + -21x + 4 = 0

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

Solving
4 + -21x + 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 + -10.5x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -10.5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -10.5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -10.5x + x2 = 0 + -2
-10.5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-10.5x + x2 = -2

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = -2 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = -2 + 27.5625

Combine like terms: -2 + 27.5625 = 25.5625
27.5625 + -10.5x + x2 = 25.5625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 25.5625

Calculate the square root of the right side: 5.055937104

Break this problem into two subproblems by setting 
(x + -5.25) equal to 5.055937104 and -5.055937104.

Subproblem 1

x + -5.25 = 5.055937104 Simplifying x + -5.25 = 5.055937104 Reorder the terms: -5.25 + x = 5.055937104 Solving -5.25 + x = 5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 5.055937104 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 5.055937104 + 5.25 x = 5.055937104 + 5.25 Combine like terms: 5.055937104 + 5.25 = 10.305937104 x = 10.305937104 Simplifying x = 10.305937104

Subproblem 2

x + -5.25 = -5.055937104 Simplifying x + -5.25 = -5.055937104 Reorder the terms: -5.25 + x = -5.055937104 Solving -5.25 + x = -5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -5.055937104 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -5.055937104 + 5.25 x = -5.055937104 + 5.25 Combine like terms: -5.055937104 + 5.25 = 0.194062896 x = 0.194062896 Simplifying x = 0.194062896

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.305937104, 0.194062896}

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