7x^2-49x-49=0

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Solution for 7x^2-49x-49=0 equation: 


Simplifying
7x2 + -49x + -49 = 0

Reorder the terms:
-49 + -49x + 7x2 = 0

Solving
-49 + -49x + 7x2 = 0

Solving for variable 'x'.

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

Ignore the factor 7.

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

Simplifying
-7 + -7x + x2 = 0

Solving
-7 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 7 + 12.25

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

Combine like terms: 7 + 12.25 = 19.25
12.25 + -7x + x2 = 19.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(x + -3.5) equal to 4.387482194 and -4.387482194.


Subproblem 1
x + -3.5 = 4.387482194

Simplifying
x + -3.5 = 4.387482194

Reorder the terms:
-3.5 + x = 4.387482194

Solving
-3.5 + x = 4.387482194

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 = 4.387482194 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 4.387482194 + 3.5
x = 4.387482194 + 3.5

Combine like terms: 4.387482194 + 3.5 = 7.887482194
x = 7.887482194

Simplifying
x = 7.887482194


Subproblem 2
x + -3.5 = -4.387482194

Simplifying
x + -3.5 = -4.387482194

Reorder the terms:
-3.5 + x = -4.387482194

Solving
-3.5 + x = -4.387482194

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 = -4.387482194 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -4.387482194 + 3.5
x = -4.387482194 + 3.5

Combine like terms: -4.387482194 + 3.5 = -0.887482194
x = -0.887482194

Simplifying
x = -0.887482194


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.887482194, -0.887482194}
Solution
x = {7.887482194, -0.887482194}

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