21x^2+28x-15=0

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Solution for 21x^2+28x-15=0 equation: 


Simplifying
21x2 + 28x + -15 = 0

Reorder the terms:
-15 + 28x + 21x2 = 0

Solving
-15 + 28x + 21x2 = 0

Solving for variable 'x'.

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

Divide each side by '21'.
-0.7142857143 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 1.333333333x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 1.333333333x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 1.333333333x + x2 = 0 + 0.7142857143
1.333333333x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
1.333333333x + x2 = 0.7142857143

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 0.7142857143 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 0.7142857143 + 0.4444444442

Combine like terms: 0.7142857143 + 0.4444444442 = 1.1587301585
0.4444444442 + 1.333333333x + x2 = 1.1587301585

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 1.1587301585

Calculate the square root of the right side: 1.076443291

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.076443291 and -1.076443291.


Subproblem 1
x + 0.6666666665 = 1.076443291

Simplifying
x + 0.6666666665 = 1.076443291

Reorder the terms:
0.6666666665 + x = 1.076443291

Solving
0.6666666665 + x = 1.076443291

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 1.076443291 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 1.076443291 + -0.6666666665
x = 1.076443291 + -0.6666666665

Combine like terms: 1.076443291 + -0.6666666665 = 0.4097766245
x = 0.4097766245

Simplifying
x = 0.4097766245


Subproblem 2
x + 0.6666666665 = -1.076443291

Simplifying
x + 0.6666666665 = -1.076443291

Reorder the terms:
0.6666666665 + x = -1.076443291

Solving
0.6666666665 + x = -1.076443291

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -1.076443291 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -1.076443291 + -0.6666666665
x = -1.076443291 + -0.6666666665

Combine like terms: -1.076443291 + -0.6666666665 = -1.7431099575
x = -1.7431099575

Simplifying
x = -1.7431099575


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4097766245, -1.7431099575}

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