3x^2+21x-75=0

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Solution for 3x^2+21x-75=0 equation: 


Simplifying
3x2 + 21x + -75 = 0

Reorder the terms:
-75 + 21x + 3x2 = 0

Solving
-75 + 21x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-25 + 7x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-25 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-25 + 7x + x2 = 0

Solving
-25 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 7x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 7x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 7x + x2 = 0 + 25
7x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
7x + x2 = 25

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 = 25 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 25 + 12.25

Combine like terms: 25 + 12.25 = 37.25
12.25 + 7x + x2 = 37.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(x + 3.5) equal to 6.103277808 and -6.103277808.


Subproblem 1
x + 3.5 = 6.103277808

Simplifying
x + 3.5 = 6.103277808

Reorder the terms:
3.5 + x = 6.103277808

Solving
3.5 + x = 6.103277808

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 = 6.103277808 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 6.103277808 + -3.5
x = 6.103277808 + -3.5

Combine like terms: 6.103277808 + -3.5 = 2.603277808
x = 2.603277808

Simplifying
x = 2.603277808


Subproblem 2
x + 3.5 = -6.103277808

Simplifying
x + 3.5 = -6.103277808

Reorder the terms:
3.5 + x = -6.103277808

Solving
3.5 + x = -6.103277808

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 = -6.103277808 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -6.103277808 + -3.5
x = -6.103277808 + -3.5

Combine like terms: -6.103277808 + -3.5 = -9.603277808
x = -9.603277808

Simplifying
x = -9.603277808


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.603277808, -9.603277808}
Solution
x = {2.603277808, -9.603277808}

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