x*x+7x=7

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Solution for x*x+7x=7 equation:


Simplifying
x * x + 7x = 7

Multiply x * x
x2 + 7x = 7

Reorder the terms:
7x + x2 = 7

Solving
7x + x2 = 7

Solving for variable 'x'.

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

Combine like terms: 7 + -7 = 0
-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 = 0.887482194
x = 0.887482194

Simplifying
x = 0.887482194


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 = -7.887482194
x = -7.887482194

Simplifying
x = -7.887482194


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

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