4x^2-23x-11=0

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Solution for 4x^2-23x-11=0 equation:


Simplifying
4x2 + -23x + -11 = 0

Reorder the terms:
-11 + -23x + 4x2 = 0

Solving
-11 + -23x + 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 + -5.75x + x2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -5.75x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -5.75x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -5.75x + x2 = 0 + 2.75
-5.75x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-5.75x + x2 = 2.75

The x term is -5.75x.  Take half its coefficient (-2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
-5.75x + 8.265625 + x2 = 2.75 + 8.265625

Reorder the terms:
8.265625 + -5.75x + x2 = 2.75 + 8.265625

Combine like terms: 2.75 + 8.265625 = 11.015625
8.265625 + -5.75x + x2 = 11.015625

Factor a perfect square on the left side:
(x + -2.875)(x + -2.875) = 11.015625

Calculate the square root of the right side: 3.318979512

Break this problem into two subproblems by setting 
(x + -2.875) equal to 3.318979512 and -3.318979512.

Subproblem 1

x + -2.875 = 3.318979512 Simplifying x + -2.875 = 3.318979512 Reorder the terms: -2.875 + x = 3.318979512 Solving -2.875 + x = 3.318979512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 3.318979512 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 3.318979512 + 2.875 x = 3.318979512 + 2.875 Combine like terms: 3.318979512 + 2.875 = 6.193979512 x = 6.193979512 Simplifying x = 6.193979512

Subproblem 2

x + -2.875 = -3.318979512 Simplifying x + -2.875 = -3.318979512 Reorder the terms: -2.875 + x = -3.318979512 Solving -2.875 + x = -3.318979512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -3.318979512 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -3.318979512 + 2.875 x = -3.318979512 + 2.875 Combine like terms: -3.318979512 + 2.875 = -0.443979512 x = -0.443979512 Simplifying x = -0.443979512

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.193979512, -0.443979512}

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