4x^2+17x+14=0

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Solution for 4x^2+17x+14=0 equation: 


Simplifying
4x2 + 17x + 14 = 0

Reorder the terms:
14 + 17x + 4x2 = 0

Solving
14 + 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'.
3.5 + 4.25x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 4.25x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 4.25x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 4.25x + x2 = 0 + -3.5
4.25x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
4.25x + x2 = -3.5

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 = -3.5 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = -3.5 + 4.515625

Combine like terms: -3.5 + 4.515625 = 1.015625
4.515625 + 4.25x + x2 = 1.015625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(x + 2.125) equal to 1.007782219 and -1.007782219.


Subproblem 1
x + 2.125 = 1.007782219

Simplifying
x + 2.125 = 1.007782219

Reorder the terms:
2.125 + x = 1.007782219

Solving
2.125 + x = 1.007782219

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 = 1.007782219 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = 1.007782219 + -2.125
x = 1.007782219 + -2.125

Combine like terms: 1.007782219 + -2.125 = -1.117217781
x = -1.117217781

Simplifying
x = -1.117217781


Subproblem 2
x + 2.125 = -1.007782219

Simplifying
x + 2.125 = -1.007782219

Reorder the terms:
2.125 + x = -1.007782219

Solving
2.125 + x = -1.007782219

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 = -1.007782219 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = -1.007782219 + -2.125
x = -1.007782219 + -2.125

Combine like terms: -1.007782219 + -2.125 = -3.132782219
x = -3.132782219

Simplifying
x = -3.132782219


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.117217781, -3.132782219}

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