4x^2-29x+12=0

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Solution for 4x^2-29x+12=0 equation:


Simplifying
4x2 + -29x + 12 = 0

Reorder the terms:
12 + -29x + 4x2 = 0

Solving
12 + -29x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
3 + -7.25x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -7.25x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -7.25x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7.25x + x2 = 0 + -3
-7.25x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-7.25x + x2 = -3

The x term is -7.25x.  Take half its coefficient (-3.625).
Square it (13.140625) and add it to both sides.

Add '13.140625' to each side of the equation.
-7.25x + 13.140625 + x2 = -3 + 13.140625

Reorder the terms:
13.140625 + -7.25x + x2 = -3 + 13.140625

Combine like terms: -3 + 13.140625 = 10.140625
13.140625 + -7.25x + x2 = 10.140625

Factor a perfect square on the left side:
(x + -3.625)(x + -3.625) = 10.140625

Calculate the square root of the right side: 3.184434801

Break this problem into two subproblems by setting 
(x + -3.625) equal to 3.184434801 and -3.184434801.

Subproblem 1

x + -3.625 = 3.184434801 Simplifying x + -3.625 = 3.184434801 Reorder the terms: -3.625 + x = 3.184434801 Solving -3.625 + x = 3.184434801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 3.184434801 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 3.184434801 + 3.625 x = 3.184434801 + 3.625 Combine like terms: 3.184434801 + 3.625 = 6.809434801 x = 6.809434801 Simplifying x = 6.809434801

Subproblem 2

x + -3.625 = -3.184434801 Simplifying x + -3.625 = -3.184434801 Reorder the terms: -3.625 + x = -3.184434801 Solving -3.625 + x = -3.184434801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -3.184434801 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -3.184434801 + 3.625 x = -3.184434801 + 3.625 Combine like terms: -3.184434801 + 3.625 = 0.440565199 x = 0.440565199 Simplifying x = 0.440565199

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.809434801, 0.440565199}

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