4x^2+x-114=0

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Solution for 4x^2+x-114=0 equation:


Simplifying
4x2 + x + -114 = 0

Reorder the terms:
-114 + x + 4x2 = 0

Solving
-114 + x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-28.5 + 0.25x + x2 = 0

Move the constant term to the right:

Add '28.5' to each side of the equation.
-28.5 + 0.25x + 28.5 + x2 = 0 + 28.5

Reorder the terms:
-28.5 + 28.5 + 0.25x + x2 = 0 + 28.5

Combine like terms: -28.5 + 28.5 = 0.0
0.0 + 0.25x + x2 = 0 + 28.5
0.25x + x2 = 0 + 28.5

Combine like terms: 0 + 28.5 = 28.5
0.25x + x2 = 28.5

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 = 28.5 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = 28.5 + 0.25

Combine like terms: 28.5 + 0.25 = 28.75
0.25 + 0.25x + x2 = 28.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 28.75

Calculate the square root of the right side: 5.361902647

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.361902647 and -5.361902647.

Subproblem 1

x + 0.5 = 5.361902647 Simplifying x + 0.5 = 5.361902647 Reorder the terms: 0.5 + x = 5.361902647 Solving 0.5 + x = 5.361902647 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 = 5.361902647 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.361902647 + -0.5 x = 5.361902647 + -0.5 Combine like terms: 5.361902647 + -0.5 = 4.861902647 x = 4.861902647 Simplifying x = 4.861902647

Subproblem 2

x + 0.5 = -5.361902647 Simplifying x + 0.5 = -5.361902647 Reorder the terms: 0.5 + x = -5.361902647 Solving 0.5 + x = -5.361902647 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 = -5.361902647 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.361902647 + -0.5 x = -5.361902647 + -0.5 Combine like terms: -5.361902647 + -0.5 = -5.861902647 x = -5.861902647 Simplifying x = -5.861902647

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.861902647, -5.861902647}

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