4x^2+13x=14

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Solution for 4x^2+13x=14 equation:


Simplifying
4x2 + 13x = 14

Reorder the terms:
13x + 4x2 = 14

Solving
13x + 4x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + 13x + 4x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 13x + 4x2 = 0

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

Divide each side by '4'.
-3.5 + 3.25x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 3.25x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 3.25x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 3.25x + x2 = 0 + 3.5
3.25x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
3.25x + x2 = 3.5

The x term is 3.25x.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25x + 2.640625 + x2 = 3.5 + 2.640625

Reorder the terms:
2.640625 + 3.25x + x2 = 3.5 + 2.640625

Combine like terms: 3.5 + 2.640625 = 6.140625
2.640625 + 3.25x + x2 = 6.140625

Factor a perfect square on the left side:
(x + 1.625)(x + 1.625) = 6.140625

Calculate the square root of the right side: 2.47802845

Break this problem into two subproblems by setting 
(x + 1.625) equal to 2.47802845 and -2.47802845.

Subproblem 1

x + 1.625 = 2.47802845 Simplifying x + 1.625 = 2.47802845 Reorder the terms: 1.625 + x = 2.47802845 Solving 1.625 + x = 2.47802845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 2.47802845 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 2.47802845 + -1.625 x = 2.47802845 + -1.625 Combine like terms: 2.47802845 + -1.625 = 0.85302845 x = 0.85302845 Simplifying x = 0.85302845

Subproblem 2

x + 1.625 = -2.47802845 Simplifying x + 1.625 = -2.47802845 Reorder the terms: 1.625 + x = -2.47802845 Solving 1.625 + x = -2.47802845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -2.47802845 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -2.47802845 + -1.625 x = -2.47802845 + -1.625 Combine like terms: -2.47802845 + -1.625 = -4.10302845 x = -4.10302845 Simplifying x = -4.10302845

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.85302845, -4.10302845}

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