4x^2+x=156

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Solution for 4x^2+x=156 equation:


Simplifying
4x2 + x = 156

Reorder the terms:
x + 4x2 = 156

Solving
x + 4x2 = 156

Solving for variable 'x'.

Reorder the terms:
-156 + x + 4x2 = 156 + -156

Combine like terms: 156 + -156 = 0
-156 + x + 4x2 = 0

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

Divide each side by '4'.
-39 + 0.25x + x2 = 0

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + 0.25x + 39 + x2 = 0 + 39

Reorder the terms:
-39 + 39 + 0.25x + x2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + 0.25x + x2 = 0 + 39
0.25x + x2 = 0 + 39

Combine like terms: 0 + 39 = 39
0.25x + x2 = 39

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 = 39 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = 39 + 0.25

Combine like terms: 39 + 0.25 = 39.25
0.25 + 0.25x + x2 = 39.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 39.25

Calculate the square root of the right side: 6.264982043

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.264982043 and -6.264982043.

Subproblem 1

x + 0.5 = 6.264982043 Simplifying x + 0.5 = 6.264982043 Reorder the terms: 0.5 + x = 6.264982043 Solving 0.5 + x = 6.264982043 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 = 6.264982043 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.264982043 + -0.5 x = 6.264982043 + -0.5 Combine like terms: 6.264982043 + -0.5 = 5.764982043 x = 5.764982043 Simplifying x = 5.764982043

Subproblem 2

x + 0.5 = -6.264982043 Simplifying x + 0.5 = -6.264982043 Reorder the terms: 0.5 + x = -6.264982043 Solving 0.5 + x = -6.264982043 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 = -6.264982043 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.264982043 + -0.5 x = -6.264982043 + -0.5 Combine like terms: -6.264982043 + -0.5 = -6.764982043 x = -6.764982043 Simplifying x = -6.764982043

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.764982043, -6.764982043}

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