x^2-7x+12.25=0

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Solution for x^2-7x+12.25=0 equation:


Simplifying
x2 + -7x + 12.25 = 0

Reorder the terms:
12.25 + -7x + x2 = 0

Solving
12.25 + -7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-12.25' to each side of the equation.
12.25 + -7x + -12.25 + x2 = 0 + -12.25

Reorder the terms:
12.25 + -12.25 + -7x + x2 = 0 + -12.25

Combine like terms: 12.25 + -12.25 = 0.00
0.00 + -7x + x2 = 0 + -12.25
-7x + x2 = 0 + -12.25

Combine like terms: 0 + -12.25 = -12.25
-7x + x2 = -12.25

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 = -12.25 + 12.25

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

Combine like terms: -12.25 + 12.25 = 0.00
12.25 + -7x + x2 = 0.00

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + -3.5) equal to 0.00 and 0.00.

Subproblem 1

x + -3.5 = 0.00 Simplifying x + -3.5 = 0.00 Reorder the terms: -3.5 + x = 0.00 Solving -3.5 + x = 0.00 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 = 0.00 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 0.00 + 3.5 x = 0.00 + 3.5 Combine like terms: 0.00 + 3.5 = 3.5 x = 3.5 Simplifying x = 3.5

Subproblem 2

x + -3.5 = 0.00 Simplifying x + -3.5 = 0.00 Reorder the terms: -3.5 + x = 0.00 Solving -3.5 + x = 0.00 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 = 0.00 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 0.00 + 3.5 x = 0.00 + 3.5 Combine like terms: 0.00 + 3.5 = 3.5 x = 3.5 Simplifying x = 3.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.5, 3.5}

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