4x^2+6x-1=0

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Solution for 4x^2+6x-1=0 equation:


Simplifying
4x2 + 6x + -1 = 0

Reorder the terms:
-1 + 6x + 4x2 = 0

Solving
-1 + 6x + 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'.
-0.25 + 1.5x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 1.5x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 1.5x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 1.5x + x2 = 0 + 0.25
1.5x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
1.5x + x2 = 0.25

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 0.25 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 0.25 + 0.5625

Combine like terms: 0.25 + 0.5625 = 0.8125
0.5625 + 1.5x + x2 = 0.8125

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
(x + 0.75) equal to 0.901387819 and -0.901387819.

Subproblem 1

x + 0.75 = 0.901387819 Simplifying x + 0.75 = 0.901387819 Reorder the terms: 0.75 + x = 0.901387819 Solving 0.75 + x = 0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 0.901387819 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.901387819 + -0.75 x = 0.901387819 + -0.75 Combine like terms: 0.901387819 + -0.75 = 0.151387819 x = 0.151387819 Simplifying x = 0.151387819

Subproblem 2

x + 0.75 = -0.901387819 Simplifying x + 0.75 = -0.901387819 Reorder the terms: 0.75 + x = -0.901387819 Solving 0.75 + x = -0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -0.901387819 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -0.901387819 + -0.75 x = -0.901387819 + -0.75 Combine like terms: -0.901387819 + -0.75 = -1.651387819 x = -1.651387819 Simplifying x = -1.651387819

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.151387819, -1.651387819}

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