0.25x^2-4x+16=0

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Solution for 0.25x^2-4x+16=0 equation:


Simplifying
0.25x2 + -4x + 16 = 0

Reorder the terms:
16 + -4x + 0.25x2 = 0

Solving
16 + -4x + 0.25x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.25 the coefficient of the squared term: 

Divide each side by '0.25'.
64 + -16x + x2 = 0

Move the constant term to the right:

Add '-64' to each side of the equation.
64 + -16x + -64 + x2 = 0 + -64

Reorder the terms:
64 + -64 + -16x + x2 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -16x + x2 = 0 + -64
-16x + x2 = 0 + -64

Combine like terms: 0 + -64 = -64
-16x + x2 = -64

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -64 + 64

Reorder the terms:
64 + -16x + x2 = -64 + 64

Combine like terms: -64 + 64 = 0
64 + -16x + x2 = 0

Factor a perfect square on the left side:
(x + -8)(x + -8) = 0

Calculate the square root of the right side: 0

Break this problem into two subproblems by setting 
(x + -8) equal to 0 and 0.

Subproblem 1

x + -8 = 0 Simplifying x + -8 = 0 Reorder the terms: -8 + x = 0 Solving -8 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8

Subproblem 2

x + -8 = 0 Simplifying x + -8 = 0 Reorder the terms: -8 + x = 0 Solving -8 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8

Solution

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

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