x^2+3.5x+6.25=7

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Solution for x^2+3.5x+6.25=7 equation: 


Simplifying
x2 + 3.5x + 6.25 = 7

Reorder the terms:
6.25 + 3.5x + x2 = 7

Solving
6.25 + 3.5x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
6.25 + -7 + 3.5x + x2 = 7 + -7

Combine like terms: 6.25 + -7 = -0.75
-0.75 + 3.5x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-0.75 + 3.5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 3.5x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 3.5x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 3.5x + x2 = 0 + 0.75
3.5x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
3.5x + x2 = 0.75

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 0.75 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 0.75 + 3.0625

Combine like terms: 0.75 + 3.0625 = 3.8125
3.0625 + 3.5x + x2 = 3.8125

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 3.8125

Calculate the square root of the right side: 1.952562419

Break this problem into two subproblems by setting 
(x + 1.75) equal to 1.952562419 and -1.952562419.


Subproblem 1
x + 1.75 = 1.952562419

Simplifying
x + 1.75 = 1.952562419

Reorder the terms:
1.75 + x = 1.952562419

Solving
1.75 + x = 1.952562419

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 1.952562419 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 1.952562419 + -1.75
x = 1.952562419 + -1.75

Combine like terms: 1.952562419 + -1.75 = 0.202562419
x = 0.202562419

Simplifying
x = 0.202562419


Subproblem 2
x + 1.75 = -1.952562419

Simplifying
x + 1.75 = -1.952562419

Reorder the terms:
1.75 + x = -1.952562419

Solving
1.75 + x = -1.952562419

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -1.952562419 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -1.952562419 + -1.75
x = -1.952562419 + -1.75

Combine like terms: -1.952562419 + -1.75 = -3.702562419
x = -3.702562419

Simplifying
x = -3.702562419


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.202562419, -3.702562419}

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