4x^2+17x-100=0

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Solution for 4x^2+17x-100=0 equation: 


Simplifying
4x2 + 17x + -100 = 0

Reorder the terms:
-100 + 17x + 4x2 = 0

Solving
-100 + 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'.
-25 + 4.25x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 4.25x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 4.25x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 4.25x + x2 = 0 + 25
4.25x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
4.25x + x2 = 25

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 = 25 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = 25 + 4.515625

Combine like terms: 25 + 4.515625 = 29.515625
4.515625 + 4.25x + x2 = 29.515625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 29.515625

Calculate the square root of the right side: 5.432828453

Break this problem into two subproblems by setting 
(x + 2.125) equal to 5.432828453 and -5.432828453.


Subproblem 1
x + 2.125 = 5.432828453

Simplifying
x + 2.125 = 5.432828453

Reorder the terms:
2.125 + x = 5.432828453

Solving
2.125 + x = 5.432828453

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 = 5.432828453 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = 5.432828453 + -2.125
x = 5.432828453 + -2.125

Combine like terms: 5.432828453 + -2.125 = 3.307828453
x = 3.307828453

Simplifying
x = 3.307828453


Subproblem 2
x + 2.125 = -5.432828453

Simplifying
x + 2.125 = -5.432828453

Reorder the terms:
2.125 + x = -5.432828453

Solving
2.125 + x = -5.432828453

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 = -5.432828453 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = -5.432828453 + -2.125
x = -5.432828453 + -2.125

Combine like terms: -5.432828453 + -2.125 = -7.557828453
x = -7.557828453

Simplifying
x = -7.557828453


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.307828453, -7.557828453}

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