4x^2+17x+12=0

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Solution for 4x^2+17x+12=0 equation: 


Simplifying
4x2 + 17x + 12 = 0

Reorder the terms:
12 + 17x + 4x2 = 0

Solving
12 + 17x + 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'.
3 + 4.25x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 4.25x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 4.25x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4.25x + x2 = 0 + -3
4.25x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
4.25x + x2 = -3

The x term is 4.25x.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25x + 4.515625 + x2 = -3 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = -3 + 4.515625

Combine like terms: -3 + 4.515625 = 1.515625
4.515625 + 4.25x + x2 = 1.515625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 1.515625

Calculate the square root of the right side: 1.231107225

Break this problem into two subproblems by setting 
(x + 2.125) equal to 1.231107225 and -1.231107225.


Subproblem 1
x + 2.125 = 1.231107225

Simplifying
x + 2.125 = 1.231107225

Reorder the terms:
2.125 + x = 1.231107225

Solving
2.125 + x = 1.231107225

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.125' to each side of the equation.
2.125 + -2.125 + x = 1.231107225 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = 1.231107225 + -2.125
x = 1.231107225 + -2.125

Combine like terms: 1.231107225 + -2.125 = -0.893892775
x = -0.893892775

Simplifying
x = -0.893892775


Subproblem 2
x + 2.125 = -1.231107225

Simplifying
x + 2.125 = -1.231107225

Reorder the terms:
2.125 + x = -1.231107225

Solving
2.125 + x = -1.231107225

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.125' to each side of the equation.
2.125 + -2.125 + x = -1.231107225 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = -1.231107225 + -2.125
x = -1.231107225 + -2.125

Combine like terms: -1.231107225 + -2.125 = -3.356107225
x = -3.356107225

Simplifying
x = -3.356107225


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.893892775, -3.356107225}

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