5x^2+17x-21=0

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Solution for 5x^2+17x-21=0 equation: 


Simplifying
5x2 + 17x + -21 = 0

Reorder the terms:
-21 + 17x + 5x2 = 0

Solving
-21 + 17x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-4.2 + 3.4x + x2 = 0

Move the constant term to the right:

Add '4.2' to each side of the equation.
-4.2 + 3.4x + 4.2 + x2 = 0 + 4.2

Reorder the terms:
-4.2 + 4.2 + 3.4x + x2 = 0 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + 3.4x + x2 = 0 + 4.2
3.4x + x2 = 0 + 4.2

Combine like terms: 0 + 4.2 = 4.2
3.4x + x2 = 4.2

The x term is 3.4x.  Take half its coefficient (1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
3.4x + 2.89 + x2 = 4.2 + 2.89

Reorder the terms:
2.89 + 3.4x + x2 = 4.2 + 2.89

Combine like terms: 4.2 + 2.89 = 7.09
2.89 + 3.4x + x2 = 7.09

Factor a perfect square on the left side:
(x + 1.7)(x + 1.7) = 7.09

Calculate the square root of the right side: 2.662705391

Break this problem into two subproblems by setting 
(x + 1.7) equal to 2.662705391 and -2.662705391.


Subproblem 1
x + 1.7 = 2.662705391

Simplifying
x + 1.7 = 2.662705391

Reorder the terms:
1.7 + x = 2.662705391

Solving
1.7 + x = 2.662705391

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = 2.662705391 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = 2.662705391 + -1.7
x = 2.662705391 + -1.7

Combine like terms: 2.662705391 + -1.7 = 0.962705391
x = 0.962705391

Simplifying
x = 0.962705391


Subproblem 2
x + 1.7 = -2.662705391

Simplifying
x + 1.7 = -2.662705391

Reorder the terms:
1.7 + x = -2.662705391

Solving
1.7 + x = -2.662705391

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = -2.662705391 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = -2.662705391 + -1.7
x = -2.662705391 + -1.7

Combine like terms: -2.662705391 + -1.7 = -4.362705391
x = -4.362705391

Simplifying
x = -4.362705391


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.962705391, -4.362705391}

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