4x^2=12x+9

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Solution for 4x^2=12x+9 equation:


Simplifying
4x2 = 12x + 9

Reorder the terms:
4x2 = 9 + 12x

Solving
4x2 = 9 + 12x

Solving for variable 'x'.

Reorder the terms:
-9 + -12x + 4x2 = 9 + 12x + -9 + -12x

Reorder the terms:
-9 + -12x + 4x2 = 9 + -9 + 12x + -12x

Combine like terms: 9 + -9 = 0
-9 + -12x + 4x2 = 0 + 12x + -12x
-9 + -12x + 4x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-9 + -12x + 4x2 = 0

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

Divide each side by '4'.
-2.25 + -3x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -3x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -3x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -3x + x2 = 0 + 2.25
-3x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-3x + x2 = 2.25

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 2.25 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 2.25 + 2.25

Combine like terms: 2.25 + 2.25 = 4.5
2.25 + -3x + x2 = 4.5

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.121320344 and -2.121320344.

Subproblem 1

x + -1.5 = 2.121320344 Simplifying x + -1.5 = 2.121320344 Reorder the terms: -1.5 + x = 2.121320344 Solving -1.5 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.121320344 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.121320344 + 1.5 x = 2.121320344 + 1.5 Combine like terms: 2.121320344 + 1.5 = 3.621320344 x = 3.621320344 Simplifying x = 3.621320344

Subproblem 2

x + -1.5 = -2.121320344 Simplifying x + -1.5 = -2.121320344 Reorder the terms: -1.5 + x = -2.121320344 Solving -1.5 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.121320344 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.121320344 + 1.5 x = -2.121320344 + 1.5 Combine like terms: -2.121320344 + 1.5 = -0.621320344 x = -0.621320344 Simplifying x = -0.621320344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.621320344, -0.621320344}

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