7x^2+24x-17=0

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Solution for 7x^2+24x-17=0 equation: 


Simplifying
7x2 + 24x + -17 = 0

Reorder the terms:
-17 + 24x + 7x2 = 0

Solving
-17 + 24x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-2.428571429 + 3.428571429x + x2 = 0

Move the constant term to the right:

Add '2.428571429' to each side of the equation.
-2.428571429 + 3.428571429x + 2.428571429 + x2 = 0 + 2.428571429

Reorder the terms:
-2.428571429 + 2.428571429 + 3.428571429x + x2 = 0 + 2.428571429

Combine like terms: -2.428571429 + 2.428571429 = 0.000000000
0.000000000 + 3.428571429x + x2 = 0 + 2.428571429
3.428571429x + x2 = 0 + 2.428571429

Combine like terms: 0 + 2.428571429 = 2.428571429
3.428571429x + x2 = 2.428571429

The x term is 3.428571429x.  Take half its coefficient (1.714285715).
Square it (2.938775513) and add it to both sides.

Add '2.938775513' to each side of the equation.
3.428571429x + 2.938775513 + x2 = 2.428571429 + 2.938775513

Reorder the terms:
2.938775513 + 3.428571429x + x2 = 2.428571429 + 2.938775513

Combine like terms: 2.428571429 + 2.938775513 = 5.367346942
2.938775513 + 3.428571429x + x2 = 5.367346942

Factor a perfect square on the left side:
(x + 1.714285715)(x + 1.714285715) = 5.367346942

Calculate the square root of the right side: 2.316753535

Break this problem into two subproblems by setting 
(x + 1.714285715) equal to 2.316753535 and -2.316753535.


Subproblem 1
x + 1.714285715 = 2.316753535

Simplifying
x + 1.714285715 = 2.316753535

Reorder the terms:
1.714285715 + x = 2.316753535

Solving
1.714285715 + x = 2.316753535

Solving for variable 'x'.

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

Add '-1.714285715' to each side of the equation.
1.714285715 + -1.714285715 + x = 2.316753535 + -1.714285715

Combine like terms: 1.714285715 + -1.714285715 = 0.000000000
0.000000000 + x = 2.316753535 + -1.714285715
x = 2.316753535 + -1.714285715

Combine like terms: 2.316753535 + -1.714285715 = 0.60246782
x = 0.60246782

Simplifying
x = 0.60246782


Subproblem 2
x + 1.714285715 = -2.316753535

Simplifying
x + 1.714285715 = -2.316753535

Reorder the terms:
1.714285715 + x = -2.316753535

Solving
1.714285715 + x = -2.316753535

Solving for variable 'x'.

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

Add '-1.714285715' to each side of the equation.
1.714285715 + -1.714285715 + x = -2.316753535 + -1.714285715

Combine like terms: 1.714285715 + -1.714285715 = 0.000000000
0.000000000 + x = -2.316753535 + -1.714285715
x = -2.316753535 + -1.714285715

Combine like terms: -2.316753535 + -1.714285715 = -4.03103925
x = -4.03103925

Simplifying
x = -4.03103925


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.60246782, -4.03103925}

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