4x^2+84x-780=0

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Solution for 4x^2+84x-780=0 equation: 


Simplifying
4x2 + 84x + -780 = 0

Reorder the terms:
-780 + 84x + 4x2 = 0

Solving
-780 + 84x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-195 + 21x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-195 + 21x + x2)' equal to zero and attempt to solve:

Simplifying
-195 + 21x + x2 = 0

Solving
-195 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '195' to each side of the equation.
-195 + 21x + 195 + x2 = 0 + 195

Reorder the terms:
-195 + 195 + 21x + x2 = 0 + 195

Combine like terms: -195 + 195 = 0
0 + 21x + x2 = 0 + 195
21x + x2 = 0 + 195

Combine like terms: 0 + 195 = 195
21x + x2 = 195

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 195 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 195 + 110.25

Combine like terms: 195 + 110.25 = 305.25
110.25 + 21x + x2 = 305.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 305.25

Calculate the square root of the right side: 17.47140521

Break this problem into two subproblems by setting 
(x + 10.5) equal to 17.47140521 and -17.47140521.


Subproblem 1
x + 10.5 = 17.47140521

Simplifying
x + 10.5 = 17.47140521

Reorder the terms:
10.5 + x = 17.47140521

Solving
10.5 + x = 17.47140521

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 17.47140521 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 17.47140521 + -10.5
x = 17.47140521 + -10.5

Combine like terms: 17.47140521 + -10.5 = 6.97140521
x = 6.97140521

Simplifying
x = 6.97140521


Subproblem 2
x + 10.5 = -17.47140521

Simplifying
x + 10.5 = -17.47140521

Reorder the terms:
10.5 + x = -17.47140521

Solving
10.5 + x = -17.47140521

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -17.47140521 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -17.47140521 + -10.5
x = -17.47140521 + -10.5

Combine like terms: -17.47140521 + -10.5 = -27.97140521
x = -27.97140521

Simplifying
x = -27.97140521


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.97140521, -27.97140521}
Solution
x = {6.97140521, -27.97140521}

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