3x^2-15x-21=0

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Solution for 3x^2-15x-21=0 equation: 


Simplifying
3x2 + -15x + -21 = 0

Reorder the terms:
-21 + -15x + 3x2 = 0

Solving
-21 + -15x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -5x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-7 + -5x + x2 = 0

Solving
-7 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -5x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -5x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5x + x2 = 0 + 7
-5x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-5x + x2 = 7

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 7 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 7 + 6.25

Combine like terms: 7 + 6.25 = 13.25
6.25 + -5x + x2 = 13.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.640054945 and -3.640054945.


Subproblem 1
x + -2.5 = 3.640054945

Simplifying
x + -2.5 = 3.640054945

Reorder the terms:
-2.5 + x = 3.640054945

Solving
-2.5 + x = 3.640054945

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 3.640054945 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 3.640054945 + 2.5
x = 3.640054945 + 2.5

Combine like terms: 3.640054945 + 2.5 = 6.140054945
x = 6.140054945

Simplifying
x = 6.140054945


Subproblem 2
x + -2.5 = -3.640054945

Simplifying
x + -2.5 = -3.640054945

Reorder the terms:
-2.5 + x = -3.640054945

Solving
-2.5 + x = -3.640054945

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -3.640054945 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -3.640054945 + 2.5
x = -3.640054945 + 2.5

Combine like terms: -3.640054945 + 2.5 = -1.140054945
x = -1.140054945

Simplifying
x = -1.140054945


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.140054945, -1.140054945}
Solution
x = {6.140054945, -1.140054945}

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