(4x^2)+x=64

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Solution for (4x^2)+x=64 equation:


Simplifying
(4x2) + x = 64

Reorder the terms:
x + (4x2) = 64

Solving
x + (4x2) = 64

Solving for variable 'x'.

Reorder the terms:
-64 + x + (4x2) = 64 + -64

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

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

Divide each side by '4'.
-16 + 0.25x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 0.25x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 0.25x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 0.25x + x2 = 0 + 16
0.25x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
0.25x + x2 = 16

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 = 16 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = 16 + 0.25

Combine like terms: 16 + 0.25 = 16.25
0.25 + 0.25x + x2 = 16.25

Factor a perfect square on the left side:
((x) + 0.5)((x) + 0.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
((x) + 0.5) equal to 4.031128874 and -4.031128874.

Subproblem 1

(x) + 0.5 = 4.031128874 Simplifying (x) + 0.5 = 4.031128874 x + 0.5 = 4.031128874 Reorder the terms: 0.5 + x = 4.031128874 Solving 0.5 + x = 4.031128874 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 = 4.031128874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.031128874 + -0.5 x = 4.031128874 + -0.5 Combine like terms: 4.031128874 + -0.5 = 3.531128874 x = 3.531128874 Simplifying x = 3.531128874

Subproblem 2

(x) + 0.5 = -4.031128874 Simplifying (x) + 0.5 = -4.031128874 x + 0.5 = -4.031128874 Reorder the terms: 0.5 + x = -4.031128874 Solving 0.5 + x = -4.031128874 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 = -4.031128874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.031128874 + -0.5 x = -4.031128874 + -0.5 Combine like terms: -4.031128874 + -0.5 = -4.531128874 x = -4.531128874 Simplifying x = -4.531128874

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.531128874, -4.531128874}

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