4x^2+13x+12=49

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Solution for 4x^2+13x+12=49 equation:


Simplifying
4x2 + 13x + 12 = 49

Reorder the terms:
12 + 13x + 4x2 = 49

Solving
12 + 13x + 4x2 = 49

Solving for variable 'x'.

Reorder the terms:
12 + -49 + 13x + 4x2 = 49 + -49

Combine like terms: 12 + -49 = -37
-37 + 13x + 4x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-37 + 13x + 4x2 = 0

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

Divide each side by '4'.
-9.25 + 3.25x + x2 = 0

Move the constant term to the right:

Add '9.25' to each side of the equation.
-9.25 + 3.25x + 9.25 + x2 = 0 + 9.25

Reorder the terms:
-9.25 + 9.25 + 3.25x + x2 = 0 + 9.25

Combine like terms: -9.25 + 9.25 = 0.00
0.00 + 3.25x + x2 = 0 + 9.25
3.25x + x2 = 0 + 9.25

Combine like terms: 0 + 9.25 = 9.25
3.25x + x2 = 9.25

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 = 9.25 + 2.640625

Reorder the terms:
2.640625 + 3.25x + x2 = 9.25 + 2.640625

Combine like terms: 9.25 + 2.640625 = 11.890625
2.640625 + 3.25x + x2 = 11.890625

Factor a perfect square on the left side:
(x + 1.625)(x + 1.625) = 11.890625

Calculate the square root of the right side: 3.448278556

Break this problem into two subproblems by setting 
(x + 1.625) equal to 3.448278556 and -3.448278556.

Subproblem 1

x + 1.625 = 3.448278556 Simplifying x + 1.625 = 3.448278556 Reorder the terms: 1.625 + x = 3.448278556 Solving 1.625 + x = 3.448278556 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 = 3.448278556 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 3.448278556 + -1.625 x = 3.448278556 + -1.625 Combine like terms: 3.448278556 + -1.625 = 1.823278556 x = 1.823278556 Simplifying x = 1.823278556

Subproblem 2

x + 1.625 = -3.448278556 Simplifying x + 1.625 = -3.448278556 Reorder the terms: 1.625 + x = -3.448278556 Solving 1.625 + x = -3.448278556 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 = -3.448278556 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -3.448278556 + -1.625 x = -3.448278556 + -1.625 Combine like terms: -3.448278556 + -1.625 = -5.073278556 x = -5.073278556 Simplifying x = -5.073278556

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.823278556, -5.073278556}

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