x^2-2.5x+1.5625=3.0625

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Solution for x^2-2.5x+1.5625=3.0625 equation: 


Simplifying
x2 + -2.5x + 1.5625 = 3.0625

Reorder the terms:
1.5625 + -2.5x + x2 = 3.0625

Solving
1.5625 + -2.5x + x2 = 3.0625

Solving for variable 'x'.

Reorder the terms:
1.5625 + -3.0625 + -2.5x + x2 = 3.0625 + -3.0625

Combine like terms: 1.5625 + -3.0625 = -1.5
-1.5 + -2.5x + x2 = 3.0625 + -3.0625

Combine like terms: 3.0625 + -3.0625 = 0.0000
-1.5 + -2.5x + x2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -2.5x + 1.5 + x2 = 0.0000 + 1.5

Reorder the terms:
-1.5 + 1.5 + -2.5x + x2 = 0.0000 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -2.5x + x2 = 0.0000 + 1.5
-2.5x + x2 = 0.0000 + 1.5

Combine like terms: 0.0000 + 1.5 = 1.5
-2.5x + x2 = 1.5

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 = 1.5 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 1.5 + 1.5625

Combine like terms: 1.5 + 1.5625 = 3.0625
1.5625 + -2.5x + x2 = 3.0625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 3.0625

Calculate the square root of the right side: 1.75

Break this problem into two subproblems by setting 
(x + -1.25) equal to 1.75 and -1.75.


Subproblem 1
x + -1.25 = 1.75

Simplifying
x + -1.25 = 1.75

Reorder the terms:
-1.25 + x = 1.75

Solving
-1.25 + x = 1.75

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 = 1.75 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 1.75 + 1.25
x = 1.75 + 1.25

Combine like terms: 1.75 + 1.25 = 3
x = 3

Simplifying
x = 3


Subproblem 2
x + -1.25 = -1.75

Simplifying
x + -1.25 = -1.75

Reorder the terms:
-1.25 + x = -1.75

Solving
-1.25 + x = -1.75

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 = -1.75 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -1.75 + 1.25
x = -1.75 + 1.25

Combine like terms: -1.75 + 1.25 = -0.5
x = -0.5

Simplifying
x = -0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3, -0.5}

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