3x^2-21x-15=0

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


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

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

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

Solving for variable 'x'.

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

Ignore the factor 3.

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

Simplifying
-5 + -7x + x2 = 0

Solving
-5 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 5 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 5 + 12.25

Combine like terms: 5 + 12.25 = 17.25
12.25 + -7x + x2 = 17.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(x + -3.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
x + -3.5 = 4.153311931

Simplifying
x + -3.5 = 4.153311931

Reorder the terms:
-3.5 + x = 4.153311931

Solving
-3.5 + x = 4.153311931

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 4.153311931 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 4.153311931 + 3.5
x = 4.153311931 + 3.5

Combine like terms: 4.153311931 + 3.5 = 7.653311931
x = 7.653311931

Simplifying
x = 7.653311931


Subproblem 2
x + -3.5 = -4.153311931

Simplifying
x + -3.5 = -4.153311931

Reorder the terms:
-3.5 + x = -4.153311931

Solving
-3.5 + x = -4.153311931

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -4.153311931 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -4.153311931 + 3.5
x = -4.153311931 + 3.5

Combine like terms: -4.153311931 + 3.5 = -0.653311931
x = -0.653311931

Simplifying
x = -0.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.653311931, -0.653311931}
Solution
x = {7.653311931, -0.653311931}

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