x^2+2.5x+6.25=7

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Solution for x^2+2.5x+6.25=7 equation: 


Simplifying
x2 + 2.5x + 6.25 = 7

Reorder the terms:
6.25 + 2.5x + x2 = 7

Solving
6.25 + 2.5x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
6.25 + -7 + 2.5x + x2 = 7 + -7

Combine like terms: 6.25 + -7 = -0.75
-0.75 + 2.5x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-0.75 + 2.5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 2.5x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 2.5x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 2.5x + x2 = 0 + 0.75
2.5x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
2.5x + x2 = 0.75

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 0.75 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 0.75 + 1.5625

Combine like terms: 0.75 + 1.5625 = 2.3125
1.5625 + 2.5x + x2 = 2.3125

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 2.3125

Calculate the square root of the right side: 1.520690633

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.520690633 and -1.520690633.


Subproblem 1
x + 1.25 = 1.520690633

Simplifying
x + 1.25 = 1.520690633

Reorder the terms:
1.25 + x = 1.520690633

Solving
1.25 + x = 1.520690633

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 1.520690633 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 1.520690633 + -1.25
x = 1.520690633 + -1.25

Combine like terms: 1.520690633 + -1.25 = 0.270690633
x = 0.270690633

Simplifying
x = 0.270690633


Subproblem 2
x + 1.25 = -1.520690633

Simplifying
x + 1.25 = -1.520690633

Reorder the terms:
1.25 + x = -1.520690633

Solving
1.25 + x = -1.520690633

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -1.520690633 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -1.520690633 + -1.25
x = -1.520690633 + -1.25

Combine like terms: -1.520690633 + -1.25 = -2.770690633
x = -2.770690633

Simplifying
x = -2.770690633


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.270690633, -2.770690633}

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