x^2+7x-4.5=0

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Solution for x^2+7x-4.5=0 equation: 


Simplifying
x2 + 7x + -4.5 = 0

Reorder the terms:
-4.5 + 7x + x2 = 0

Solving
-4.5 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 7x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 7x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 7x + x2 = 0 + 4.5
7x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
7x + x2 = 4.5

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 = 4.5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 4.5 + 12.25

Combine like terms: 4.5 + 12.25 = 16.75
12.25 + 7x + x2 = 16.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 16.75

Calculate the square root of the right side: 4.092676386

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.092676386 and -4.092676386.


Subproblem 1
x + 3.5 = 4.092676386

Simplifying
x + 3.5 = 4.092676386

Reorder the terms:
3.5 + x = 4.092676386

Solving
3.5 + x = 4.092676386

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 = 4.092676386 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 4.092676386 + -3.5
x = 4.092676386 + -3.5

Combine like terms: 4.092676386 + -3.5 = 0.592676386
x = 0.592676386

Simplifying
x = 0.592676386


Subproblem 2
x + 3.5 = -4.092676386

Simplifying
x + 3.5 = -4.092676386

Reorder the terms:
3.5 + x = -4.092676386

Solving
3.5 + x = -4.092676386

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 = -4.092676386 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -4.092676386 + -3.5
x = -4.092676386 + -3.5

Combine like terms: -4.092676386 + -3.5 = -7.592676386
x = -7.592676386

Simplifying
x = -7.592676386


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.592676386, -7.592676386}

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