x(-4x-11)=-4

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Solution for x(-4x-11)=-4 equation:


Simplifying
x(-4x + -11) = -4

Reorder the terms:
x(-11 + -4x) = -4
(-11 * x + -4x * x) = -4
(-11x + -4x2) = -4

Solving
-11x + -4x2 = -4

Solving for variable 'x'.

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

Combine like terms: -4 + 4 = 0
4 + -11x + -4x2 = 0

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

Divide each side by '-4'.
-1 + 2.75x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2.75x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 2.75x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2.75x + x2 = 0 + 1
2.75x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2.75x + x2 = 1

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 + 1.890625

Reorder the terms:
1.890625 + 2.75x + x2 = 1 + 1.890625

Combine like terms: 1 + 1.890625 = 2.890625
1.890625 + 2.75x + x2 = 2.890625

Factor a perfect square on the left side:
(x + 1.375)(x + 1.375) = 2.890625

Calculate the square root of the right side: 1.700183814

Break this problem into two subproblems by setting 
(x + 1.375) equal to 1.700183814 and -1.700183814.

Subproblem 1

x + 1.375 = 1.700183814 Simplifying x + 1.375 = 1.700183814 Reorder the terms: 1.375 + x = 1.700183814 Solving 1.375 + x = 1.700183814 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 = 1.700183814 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 1.700183814 + -1.375 x = 1.700183814 + -1.375 Combine like terms: 1.700183814 + -1.375 = 0.325183814 x = 0.325183814 Simplifying x = 0.325183814

Subproblem 2

x + 1.375 = -1.700183814 Simplifying x + 1.375 = -1.700183814 Reorder the terms: 1.375 + x = -1.700183814 Solving 1.375 + x = -1.700183814 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 = -1.700183814 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -1.700183814 + -1.375 x = -1.700183814 + -1.375 Combine like terms: -1.700183814 + -1.375 = -3.075183814 x = -3.075183814 Simplifying x = -3.075183814

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.325183814, -3.075183814}

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