x^2-8.5x+4=0

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Solution for x^2-8.5x+4=0 equation:


Simplifying
x2 + -8.5x + 4 = 0

Reorder the terms:
4 + -8.5x + x2 = 0

Solving
4 + -8.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -8.5x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -8.5x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -8.5x + x2 = 0 + -4
-8.5x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-8.5x + x2 = -4

The x term is -8.5x.  Take half its coefficient (-4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
-8.5x + 18.0625 + x2 = -4 + 18.0625

Reorder the terms:
18.0625 + -8.5x + x2 = -4 + 18.0625

Combine like terms: -4 + 18.0625 = 14.0625
18.0625 + -8.5x + x2 = 14.0625

Factor a perfect square on the left side:
(x + -4.25)(x + -4.25) = 14.0625

Calculate the square root of the right side: 3.75

Break this problem into two subproblems by setting 
(x + -4.25) equal to 3.75 and -3.75.

Subproblem 1

x + -4.25 = 3.75 Simplifying x + -4.25 = 3.75 Reorder the terms: -4.25 + x = 3.75 Solving -4.25 + x = 3.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 3.75 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 3.75 + 4.25 x = 3.75 + 4.25 Combine like terms: 3.75 + 4.25 = 8 x = 8 Simplifying x = 8

Subproblem 2

x + -4.25 = -3.75 Simplifying x + -4.25 = -3.75 Reorder the terms: -4.25 + x = -3.75 Solving -4.25 + x = -3.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -3.75 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -3.75 + 4.25 x = -3.75 + 4.25 Combine like terms: -3.75 + 4.25 = 0.5 x = 0.5 Simplifying x = 0.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8, 0.5}

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