9x-4=4x^2

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


Simplifying
9x + -4 = 4x2

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

Solving
-4 + 9x = 4x2

Solving for variable 'x'.

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

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
1 + -2.25x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.25x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -2.25x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.25x + x2 = 0 + -1
-2.25x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.25x + x2 = -1

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = -1 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = -1 + 1.265625

Combine like terms: -1 + 1.265625 = 0.265625
1.265625 + -2.25x + x2 = 0.265625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(x + -1.125) equal to 0.515388203 and -0.515388203.

Subproblem 1

x + -1.125 = 0.515388203 Simplifying x + -1.125 = 0.515388203 Reorder the terms: -1.125 + x = 0.515388203 Solving -1.125 + x = 0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 0.515388203 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 0.515388203 + 1.125 x = 0.515388203 + 1.125 Combine like terms: 0.515388203 + 1.125 = 1.640388203 x = 1.640388203 Simplifying x = 1.640388203

Subproblem 2

x + -1.125 = -0.515388203 Simplifying x + -1.125 = -0.515388203 Reorder the terms: -1.125 + x = -0.515388203 Solving -1.125 + x = -0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -0.515388203 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -0.515388203 + 1.125 x = -0.515388203 + 1.125 Combine like terms: -0.515388203 + 1.125 = 0.609611797 x = 0.609611797 Simplifying x = 0.609611797

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.640388203, 0.609611797}

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