9x^2=4x+4

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Solution for 9x^2=4x+4 equation:


Simplifying
9x2 = 4x + 4

Reorder the terms:
9x2 = 4 + 4x

Solving
9x2 = 4 + 4x

Solving for variable 'x'.

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

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

Combine like terms: 4 + -4 = 0
-4 + -4x + 9x2 = 0 + 4x + -4x
-4 + -4x + 9x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-4 + -4x + 9x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

The x term is -0.4444444444x.  Take half its coefficient (-0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
-0.4444444444x + 0.04938271604 + x2 = 0.4444444444 + 0.04938271604

Reorder the terms:
0.04938271604 + -0.4444444444x + x2 = 0.4444444444 + 0.04938271604

Combine like terms: 0.4444444444 + 0.04938271604 = 0.49382716044
0.04938271604 + -0.4444444444x + x2 = 0.49382716044

Factor a perfect square on the left side:
(x + -0.2222222222)(x + -0.2222222222) = 0.49382716044

Calculate the square root of the right side: 0.702728369

Break this problem into two subproblems by setting 
(x + -0.2222222222) equal to 0.702728369 and -0.702728369.

Subproblem 1

x + -0.2222222222 = 0.702728369 Simplifying x + -0.2222222222 = 0.702728369 Reorder the terms: -0.2222222222 + x = 0.702728369 Solving -0.2222222222 + x = 0.702728369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 0.702728369 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 0.702728369 + 0.2222222222 x = 0.702728369 + 0.2222222222 Combine like terms: 0.702728369 + 0.2222222222 = 0.9249505912 x = 0.9249505912 Simplifying x = 0.9249505912

Subproblem 2

x + -0.2222222222 = -0.702728369 Simplifying x + -0.2222222222 = -0.702728369 Reorder the terms: -0.2222222222 + x = -0.702728369 Solving -0.2222222222 + x = -0.702728369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -0.702728369 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -0.702728369 + 0.2222222222 x = -0.702728369 + 0.2222222222 Combine like terms: -0.702728369 + 0.2222222222 = -0.4805061468 x = -0.4805061468 Simplifying x = -0.4805061468

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9249505912, -0.4805061468}

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