9x^2-16x+4=0

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Solution for 9x^2-16x+4=0 equation:


Simplifying
9x2 + -16x + 4 = 0

Reorder the terms:
4 + -16x + 9x2 = 0

Solving
4 + -16x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
0.4444444444 + -1.777777778x + x2 = 0

Move the constant term to the right:

Add '-0.4444444444' to each side of the equation.
0.4444444444 + -1.777777778x + -0.4444444444 + x2 = 0 + -0.4444444444

Reorder the terms:
0.4444444444 + -0.4444444444 + -1.777777778x + x2 = 0 + -0.4444444444

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
0.0000000000 + -1.777777778x + x2 = 0 + -0.4444444444
-1.777777778x + x2 = 0 + -0.4444444444

Combine like terms: 0 + -0.4444444444 = -0.4444444444
-1.777777778x + x2 = -0.4444444444

The x term is -1.777777778x.  Take half its coefficient (-0.888888889).
Square it (0.7901234570) and add it to both sides.

Add '0.7901234570' to each side of the equation.
-1.777777778x + 0.7901234570 + x2 = -0.4444444444 + 0.7901234570

Reorder the terms:
0.7901234570 + -1.777777778x + x2 = -0.4444444444 + 0.7901234570

Combine like terms: -0.4444444444 + 0.7901234570 = 0.3456790126
0.7901234570 + -1.777777778x + x2 = 0.3456790126

Factor a perfect square on the left side:
(x + -0.888888889)(x + -0.888888889) = 0.3456790126

Calculate the square root of the right side: 0.587944736

Break this problem into two subproblems by setting 
(x + -0.888888889) equal to 0.587944736 and -0.587944736.

Subproblem 1

x + -0.888888889 = 0.587944736 Simplifying x + -0.888888889 = 0.587944736 Reorder the terms: -0.888888889 + x = 0.587944736 Solving -0.888888889 + x = 0.587944736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = 0.587944736 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 0.587944736 + 0.888888889 x = 0.587944736 + 0.888888889 Combine like terms: 0.587944736 + 0.888888889 = 1.476833625 x = 1.476833625 Simplifying x = 1.476833625

Subproblem 2

x + -0.888888889 = -0.587944736 Simplifying x + -0.888888889 = -0.587944736 Reorder the terms: -0.888888889 + x = -0.587944736 Solving -0.888888889 + x = -0.587944736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = -0.587944736 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -0.587944736 + 0.888888889 x = -0.587944736 + 0.888888889 Combine like terms: -0.587944736 + 0.888888889 = 0.300944153 x = 0.300944153 Simplifying x = 0.300944153

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.476833625, 0.300944153}

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