4x^2+12x-11=0

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Solution for 4x^2+12x-11=0 equation:


Simplifying
4x2 + 12x + -11 = 0

Reorder the terms:
-11 + 12x + 4x2 = 0

Solving
-11 + 12x + 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'.
-2.75 + 3x + x2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + 3x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + 3x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + 3x + x2 = 0 + 2.75
3x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
3x + x2 = 2.75

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 2.75 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2.75 + 2.25

Combine like terms: 2.75 + 2.25 = 5
2.25 + 3x + x2 = 5

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.236067978 and -2.236067978.

Subproblem 1

x + 1.5 = 2.236067978 Simplifying x + 1.5 = 2.236067978 Reorder the terms: 1.5 + x = 2.236067978 Solving 1.5 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.236067978 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.236067978 + -1.5 x = 2.236067978 + -1.5 Combine like terms: 2.236067978 + -1.5 = 0.736067978 x = 0.736067978 Simplifying x = 0.736067978

Subproblem 2

x + 1.5 = -2.236067978 Simplifying x + 1.5 = -2.236067978 Reorder the terms: 1.5 + x = -2.236067978 Solving 1.5 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.236067978 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.236067978 + -1.5 x = -2.236067978 + -1.5 Combine like terms: -2.236067978 + -1.5 = -3.736067978 x = -3.736067978 Simplifying x = -3.736067978

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.736067978, -3.736067978}

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