2x^2+13x=4

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


Simplifying
2x2 + 13x = 4

Reorder the terms:
13x + 2x2 = 4

Solving
13x + 2x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 13x + 2x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 13x + 2x2 = 0

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

Divide each side by '2'.
-2 + 6.5x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 6.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 6.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 6.5x + x2 = 0 + 2
6.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
6.5x + x2 = 2

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = 2 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 2 + 10.5625

Combine like terms: 2 + 10.5625 = 12.5625
10.5625 + 6.5x + x2 = 12.5625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(x + 3.25) equal to 3.54436172 and -3.54436172.

Subproblem 1

x + 3.25 = 3.54436172 Simplifying x + 3.25 = 3.54436172 Reorder the terms: 3.25 + x = 3.54436172 Solving 3.25 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 3.54436172 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.54436172 + -3.25 x = 3.54436172 + -3.25 Combine like terms: 3.54436172 + -3.25 = 0.29436172 x = 0.29436172 Simplifying x = 0.29436172

Subproblem 2

x + 3.25 = -3.54436172 Simplifying x + 3.25 = -3.54436172 Reorder the terms: 3.25 + x = -3.54436172 Solving 3.25 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -3.54436172 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.54436172 + -3.25 x = -3.54436172 + -3.25 Combine like terms: -3.54436172 + -3.25 = -6.79436172 x = -6.79436172 Simplifying x = -6.79436172

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.29436172, -6.79436172}

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