25x^2-4+11x=-11x

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Solution for 25x^2-4+11x=-11x equation:


Simplifying
25x2 + -4 + 11x = -11x

Reorder the terms:
-4 + 11x + 25x2 = -11x

Solving
-4 + 11x + 25x2 = -11x

Solving for variable 'x'.

Reorder the terms:
-4 + 11x + 11x + 25x2 = -11x + 11x

Combine like terms: 11x + 11x = 22x
-4 + 22x + 25x2 = -11x + 11x

Combine like terms: -11x + 11x = 0
-4 + 22x + 25x2 = 0

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

Divide each side by '25'.
-0.16 + 0.88x + x2 = 0

Move the constant term to the right:

Add '0.16' to each side of the equation.
-0.16 + 0.88x + 0.16 + x2 = 0 + 0.16

Reorder the terms:
-0.16 + 0.16 + 0.88x + x2 = 0 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + 0.88x + x2 = 0 + 0.16
0.88x + x2 = 0 + 0.16

Combine like terms: 0 + 0.16 = 0.16
0.88x + x2 = 0.16

The x term is 0.88x.  Take half its coefficient (0.44).
Square it (0.1936) and add it to both sides.

Add '0.1936' to each side of the equation.
0.88x + 0.1936 + x2 = 0.16 + 0.1936

Reorder the terms:
0.1936 + 0.88x + x2 = 0.16 + 0.1936

Combine like terms: 0.16 + 0.1936 = 0.3536
0.1936 + 0.88x + x2 = 0.3536

Factor a perfect square on the left side:
(x + 0.44)(x + 0.44) = 0.3536

Calculate the square root of the right side: 0.59464275

Break this problem into two subproblems by setting 
(x + 0.44) equal to 0.59464275 and -0.59464275.

Subproblem 1

x + 0.44 = 0.59464275 Simplifying x + 0.44 = 0.59464275 Reorder the terms: 0.44 + x = 0.59464275 Solving 0.44 + x = 0.59464275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.44' to each side of the equation. 0.44 + -0.44 + x = 0.59464275 + -0.44 Combine like terms: 0.44 + -0.44 = 0.00 0.00 + x = 0.59464275 + -0.44 x = 0.59464275 + -0.44 Combine like terms: 0.59464275 + -0.44 = 0.15464275 x = 0.15464275 Simplifying x = 0.15464275

Subproblem 2

x + 0.44 = -0.59464275 Simplifying x + 0.44 = -0.59464275 Reorder the terms: 0.44 + x = -0.59464275 Solving 0.44 + x = -0.59464275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.44' to each side of the equation. 0.44 + -0.44 + x = -0.59464275 + -0.44 Combine like terms: 0.44 + -0.44 = 0.00 0.00 + x = -0.59464275 + -0.44 x = -0.59464275 + -0.44 Combine like terms: -0.59464275 + -0.44 = -1.03464275 x = -1.03464275 Simplifying x = -1.03464275

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.15464275, -1.03464275}

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