4x^2-11x-6=0

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Solution for 4x^2-11x-6=0 equation:


Simplifying
4x2 + -11x + -6 = 0

Reorder the terms:
-6 + -11x + 4x2 = 0

Solving
-6 + -11x + 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'.
-1.5 + -2.75x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -2.75x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -2.75x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -2.75x + x2 = 0 + 1.5
-2.75x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-2.75x + x2 = 1.5

The x term is -2.75x.  Take half its coefficient (-1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
-2.75x + 1.890625 + x2 = 1.5 + 1.890625

Reorder the terms:
1.890625 + -2.75x + x2 = 1.5 + 1.890625

Combine like terms: 1.5 + 1.890625 = 3.390625
1.890625 + -2.75x + x2 = 3.390625

Factor a perfect square on the left side:
(x + -1.375)(x + -1.375) = 3.390625

Calculate the square root of the right side: 1.841364983

Break this problem into two subproblems by setting 
(x + -1.375) equal to 1.841364983 and -1.841364983.

Subproblem 1

x + -1.375 = 1.841364983 Simplifying x + -1.375 = 1.841364983 Reorder the terms: -1.375 + x = 1.841364983 Solving -1.375 + x = 1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 1.841364983 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.841364983 + 1.375 x = 1.841364983 + 1.375 Combine like terms: 1.841364983 + 1.375 = 3.216364983 x = 3.216364983 Simplifying x = 3.216364983

Subproblem 2

x + -1.375 = -1.841364983 Simplifying x + -1.375 = -1.841364983 Reorder the terms: -1.375 + x = -1.841364983 Solving -1.375 + x = -1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -1.841364983 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.841364983 + 1.375 x = -1.841364983 + 1.375 Combine like terms: -1.841364983 + 1.375 = -0.466364983 x = -0.466364983 Simplifying x = -0.466364983

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.216364983, -0.466364983}

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