x^2=6.5x-10

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Solution for x^2=6.5x-10 equation: 


Simplifying
x2 = 6.5x + -10

Reorder the terms:
x2 = -10 + 6.5x

Solving
x2 = -10 + 6.5x

Solving for variable 'x'.

Reorder the terms:
10 + -6.5x + x2 = -10 + 6.5x + 10 + -6.5x

Reorder the terms:
10 + -6.5x + x2 = -10 + 10 + 6.5x + -6.5x

Combine like terms: -10 + 10 = 0
10 + -6.5x + x2 = 0 + 6.5x + -6.5x
10 + -6.5x + x2 = 6.5x + -6.5x

Combine like terms: 6.5x + -6.5x = 0.0
10 + -6.5x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -6.5x + -10 + x2 = 0.0 + -10

Reorder the terms:
10 + -10 + -6.5x + x2 = 0.0 + -10

Combine like terms: 10 + -10 = 0
0 + -6.5x + x2 = 0.0 + -10
-6.5x + x2 = 0.0 + -10

Combine like terms: 0.0 + -10 = -10
-6.5x + x2 = -10

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = -10 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = -10 + 10.5625

Combine like terms: -10 + 10.5625 = 0.5625
10.5625 + -6.5x + x2 = 0.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 0.5625

Calculate the square root of the right side: 0.75

Break this problem into two subproblems by setting 
(x + -3.25) equal to 0.75 and -0.75.


Subproblem 1
x + -3.25 = 0.75

Simplifying
x + -3.25 = 0.75

Reorder the terms:
-3.25 + x = 0.75

Solving
-3.25 + x = 0.75

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 0.75 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 0.75 + 3.25
x = 0.75 + 3.25

Combine like terms: 0.75 + 3.25 = 4
x = 4

Simplifying
x = 4


Subproblem 2
x + -3.25 = -0.75

Simplifying
x + -3.25 = -0.75

Reorder the terms:
-3.25 + x = -0.75

Solving
-3.25 + x = -0.75

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -0.75 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -0.75 + 3.25
x = -0.75 + 3.25

Combine like terms: -0.75 + 3.25 = 2.5
x = 2.5

Simplifying
x = 2.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4, 2.5}

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