4x^2+x+1=64

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Solution for 4x^2+x+1=64 equation:


Simplifying
4x2 + x + 1 = 64

Reorder the terms:
1 + x + 4x2 = 64

Solving
1 + x + 4x2 = 64

Solving for variable 'x'.

Reorder the terms:
1 + -64 + x + 4x2 = 64 + -64

Combine like terms: 1 + -64 = -63
-63 + x + 4x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-63 + x + 4x2 = 0

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

Divide each side by '4'.
-15.75 + 0.25x + x2 = 0

Move the constant term to the right:

Add '15.75' to each side of the equation.
-15.75 + 0.25x + 15.75 + x2 = 0 + 15.75

Reorder the terms:
-15.75 + 15.75 + 0.25x + x2 = 0 + 15.75

Combine like terms: -15.75 + 15.75 = 0.00
0.00 + 0.25x + x2 = 0 + 15.75
0.25x + x2 = 0 + 15.75

Combine like terms: 0 + 15.75 = 15.75
0.25x + x2 = 15.75

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25x + 0.25 + x2 = 15.75 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = 15.75 + 0.25

Combine like terms: 15.75 + 0.25 = 16
0.25 + 0.25x + x2 = 16

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4 and -4.


Subproblem 1
x + 0.5 = 4

Simplifying
x + 0.5 = 4

Reorder the terms:
0.5 + x = 4

Solving
0.5 + x = 4

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 4 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4 + -0.5
x = 4 + -0.5

Combine like terms: 4 + -0.5 = 3.5
x = 3.5

Simplifying
x = 3.5


Subproblem 2
x + 0.5 = -4

Simplifying
x + 0.5 = -4

Reorder the terms:
0.5 + x = -4

Solving
0.5 + x = -4

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -4 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4 + -0.5
x = -4 + -0.5

Combine like terms: -4 + -0.5 = -4.5
x = -4.5

Simplifying
x = -4.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5, -4.5}

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