15x^2+11x-21=0

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Solution for 15x^2+11x-21=0 equation: 


Simplifying
15x2 + 11x + -21 = 0

Reorder the terms:
-21 + 11x + 15x2 = 0

Solving
-21 + 11x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-1.4 + 0.7333333333x + x2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + 0.7333333333x + 1.4 + x2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + 0.7333333333x + x2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + 0.7333333333x + x2 = 0 + 1.4
0.7333333333x + x2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
0.7333333333x + x2 = 1.4

The x term is 0.7333333333x.  Take half its coefficient (0.3666666667).
Square it (0.1344444445) and add it to both sides.

Add '0.1344444445' to each side of the equation.
0.7333333333x + 0.1344444445 + x2 = 1.4 + 0.1344444445

Reorder the terms:
0.1344444445 + 0.7333333333x + x2 = 1.4 + 0.1344444445

Combine like terms: 1.4 + 0.1344444445 = 1.5344444445
0.1344444445 + 0.7333333333x + x2 = 1.5344444445

Factor a perfect square on the left side:
(x + 0.3666666667)(x + 0.3666666667) = 1.5344444445

Calculate the square root of the right side: 1.238726945

Break this problem into two subproblems by setting 
(x + 0.3666666667) equal to 1.238726945 and -1.238726945.


Subproblem 1
x + 0.3666666667 = 1.238726945

Simplifying
x + 0.3666666667 = 1.238726945

Reorder the terms:
0.3666666667 + x = 1.238726945

Solving
0.3666666667 + x = 1.238726945

Solving for variable 'x'.

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

Add '-0.3666666667' to each side of the equation.
0.3666666667 + -0.3666666667 + x = 1.238726945 + -0.3666666667

Combine like terms: 0.3666666667 + -0.3666666667 = 0.0000000000
0.0000000000 + x = 1.238726945 + -0.3666666667
x = 1.238726945 + -0.3666666667

Combine like terms: 1.238726945 + -0.3666666667 = 0.8720602783
x = 0.8720602783

Simplifying
x = 0.8720602783


Subproblem 2
x + 0.3666666667 = -1.238726945

Simplifying
x + 0.3666666667 = -1.238726945

Reorder the terms:
0.3666666667 + x = -1.238726945

Solving
0.3666666667 + x = -1.238726945

Solving for variable 'x'.

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

Add '-0.3666666667' to each side of the equation.
0.3666666667 + -0.3666666667 + x = -1.238726945 + -0.3666666667

Combine like terms: 0.3666666667 + -0.3666666667 = 0.0000000000
0.0000000000 + x = -1.238726945 + -0.3666666667
x = -1.238726945 + -0.3666666667

Combine like terms: -1.238726945 + -0.3666666667 = -1.6053936117
x = -1.6053936117

Simplifying
x = -1.6053936117


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8720602783, -1.6053936117}

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