20x^2+5=21x

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Solution for 20x^2+5=21x equation:


Simplifying
20x2 + 5 = 21x

Reorder the terms:
5 + 20x2 = 21x

Solving
5 + 20x2 = 21x

Solving for variable 'x'.

Reorder the terms:
5 + -21x + 20x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
5 + -21x + 20x2 = 0

Begin completing the square.  Divide all terms by
20 the coefficient of the squared term: 

Divide each side by '20'.
0.25 + -1.05x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.05x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.05x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.05x + x2 = 0 + -0.25
-1.05x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.05x + x2 = -0.25

The x term is -1.05x.  Take half its coefficient (-0.525).
Square it (0.275625) and add it to both sides.

Add '0.275625' to each side of the equation.
-1.05x + 0.275625 + x2 = -0.25 + 0.275625

Reorder the terms:
0.275625 + -1.05x + x2 = -0.25 + 0.275625

Combine like terms: -0.25 + 0.275625 = 0.025625
0.275625 + -1.05x + x2 = 0.025625

Factor a perfect square on the left side:
(x + -0.525)(x + -0.525) = 0.025625

Calculate the square root of the right side: 0.160078106

Break this problem into two subproblems by setting 
(x + -0.525) equal to 0.160078106 and -0.160078106.

Subproblem 1

x + -0.525 = 0.160078106 Simplifying x + -0.525 = 0.160078106 Reorder the terms: -0.525 + x = 0.160078106 Solving -0.525 + x = 0.160078106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.525' to each side of the equation. -0.525 + 0.525 + x = 0.160078106 + 0.525 Combine like terms: -0.525 + 0.525 = 0.000 0.000 + x = 0.160078106 + 0.525 x = 0.160078106 + 0.525 Combine like terms: 0.160078106 + 0.525 = 0.685078106 x = 0.685078106 Simplifying x = 0.685078106

Subproblem 2

x + -0.525 = -0.160078106 Simplifying x + -0.525 = -0.160078106 Reorder the terms: -0.525 + x = -0.160078106 Solving -0.525 + x = -0.160078106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.525' to each side of the equation. -0.525 + 0.525 + x = -0.160078106 + 0.525 Combine like terms: -0.525 + 0.525 = 0.000 0.000 + x = -0.160078106 + 0.525 x = -0.160078106 + 0.525 Combine like terms: -0.160078106 + 0.525 = 0.364921894 x = 0.364921894 Simplifying x = 0.364921894

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.685078106, 0.364921894}

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