x^2-9x+2-.25=0.25

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Solution for x^2-9x+2-.25=0.25 equation:


Simplifying
x2 + -9x + 2 + -0.25 = 0.25

Reorder the terms:
2 + -0.25 + -9x + x2 = 0.25

Combine like terms: 2 + -0.25 = 1.75
1.75 + -9x + x2 = 0.25

Solving
1.75 + -9x + x2 = 0.25

Solving for variable 'x'.

Reorder the terms:
1.75 + -0.25 + -9x + x2 = 0.25 + -0.25

Combine like terms: 1.75 + -0.25 = 1.5
1.5 + -9x + x2 = 0.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
1.5 + -9x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -9x + -1.5 + x2 = 0.00 + -1.5

Reorder the terms:
1.5 + -1.5 + -9x + x2 = 0.00 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -9x + x2 = 0.00 + -1.5
-9x + x2 = 0.00 + -1.5

Combine like terms: 0.00 + -1.5 = -1.5
-9x + x2 = -1.5

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -1.5 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -1.5 + 20.25

Combine like terms: -1.5 + 20.25 = 18.75
20.25 + -9x + x2 = 18.75

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 18.75

Calculate the square root of the right side: 4.330127019

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.330127019 and -4.330127019.

Subproblem 1

x + -4.5 = 4.330127019 Simplifying x + -4.5 = 4.330127019 Reorder the terms: -4.5 + x = 4.330127019 Solving -4.5 + x = 4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.330127019 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.330127019 + 4.5 x = 4.330127019 + 4.5 Combine like terms: 4.330127019 + 4.5 = 8.830127019 x = 8.830127019 Simplifying x = 8.830127019

Subproblem 2

x + -4.5 = -4.330127019 Simplifying x + -4.5 = -4.330127019 Reorder the terms: -4.5 + x = -4.330127019 Solving -4.5 + x = -4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.330127019 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.330127019 + 4.5 x = -4.330127019 + 4.5 Combine like terms: -4.330127019 + 4.5 = 0.169872981 x = 0.169872981 Simplifying x = 0.169872981

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.830127019, 0.169872981}

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