9x^2=4x+8

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Solution for 9x^2=4x+8 equation:


Simplifying
9x2 = 4x + 8

Reorder the terms:
9x2 = 8 + 4x

Solving
9x2 = 8 + 4x

Solving for variable 'x'.

Reorder the terms:
-8 + -4x + 9x2 = 8 + 4x + -8 + -4x

Reorder the terms:
-8 + -4x + 9x2 = 8 + -8 + 4x + -4x

Combine like terms: 8 + -8 = 0
-8 + -4x + 9x2 = 0 + 4x + -4x
-8 + -4x + 9x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-8 + -4x + 9x2 = 0

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

Divide each side by '9'.
-0.8888888889 + -0.4444444444x + x2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + -0.4444444444x + 0.8888888889 + x2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + -0.4444444444x + x2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + -0.4444444444x + x2 = 0 + 0.8888888889
-0.4444444444x + x2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
-0.4444444444x + x2 = 0.8888888889

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 = 0.8888888889 + 0.04938271604

Reorder the terms:
0.04938271604 + -0.4444444444x + x2 = 0.8888888889 + 0.04938271604

Combine like terms: 0.8888888889 + 0.04938271604 = 0.93827160494
0.04938271604 + -0.4444444444x + x2 = 0.93827160494

Factor a perfect square on the left side:
(x + -0.2222222222)(x + -0.2222222222) = 0.93827160494

Calculate the square root of the right side: 0.96864421

Break this problem into two subproblems by setting 
(x + -0.2222222222) equal to 0.96864421 and -0.96864421.

Subproblem 1

x + -0.2222222222 = 0.96864421 Simplifying x + -0.2222222222 = 0.96864421 Reorder the terms: -0.2222222222 + x = 0.96864421 Solving -0.2222222222 + x = 0.96864421 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 = 0.96864421 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 0.96864421 + 0.2222222222 x = 0.96864421 + 0.2222222222 Combine like terms: 0.96864421 + 0.2222222222 = 1.1908664322 x = 1.1908664322 Simplifying x = 1.1908664322

Subproblem 2

x + -0.2222222222 = -0.96864421 Simplifying x + -0.2222222222 = -0.96864421 Reorder the terms: -0.2222222222 + x = -0.96864421 Solving -0.2222222222 + x = -0.96864421 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 = -0.96864421 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -0.96864421 + 0.2222222222 x = -0.96864421 + 0.2222222222 Combine like terms: -0.96864421 + 0.2222222222 = -0.7464219878 x = -0.7464219878 Simplifying x = -0.7464219878

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.1908664322, -0.7464219878}

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