16x^2+29x-12=0

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Solution for 16x^2+29x-12=0 equation:


Simplifying
16x2 + 29x + -12 = 0

Reorder the terms:
-12 + 29x + 16x2 = 0

Solving
-12 + 29x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
-0.75 + 1.8125x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 1.8125x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 1.8125x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 1.8125x + x2 = 0 + 0.75
1.8125x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
1.8125x + x2 = 0.75

The x term is 1.8125x.  Take half its coefficient (0.90625).
Square it (0.8212890625) and add it to both sides.

Add '0.8212890625' to each side of the equation.
1.8125x + 0.8212890625 + x2 = 0.75 + 0.8212890625

Reorder the terms:
0.8212890625 + 1.8125x + x2 = 0.75 + 0.8212890625

Combine like terms: 0.75 + 0.8212890625 = 1.5712890625
0.8212890625 + 1.8125x + x2 = 1.5712890625

Factor a perfect square on the left side:
(x + 0.90625)(x + 0.90625) = 1.5712890625

Calculate the square root of the right side: 1.253510695

Break this problem into two subproblems by setting 
(x + 0.90625) equal to 1.253510695 and -1.253510695.

Subproblem 1

x + 0.90625 = 1.253510695 Simplifying x + 0.90625 = 1.253510695 Reorder the terms: 0.90625 + x = 1.253510695 Solving 0.90625 + x = 1.253510695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.90625' to each side of the equation. 0.90625 + -0.90625 + x = 1.253510695 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + x = 1.253510695 + -0.90625 x = 1.253510695 + -0.90625 Combine like terms: 1.253510695 + -0.90625 = 0.347260695 x = 0.347260695 Simplifying x = 0.347260695

Subproblem 2

x + 0.90625 = -1.253510695 Simplifying x + 0.90625 = -1.253510695 Reorder the terms: 0.90625 + x = -1.253510695 Solving 0.90625 + x = -1.253510695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.90625' to each side of the equation. 0.90625 + -0.90625 + x = -1.253510695 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + x = -1.253510695 + -0.90625 x = -1.253510695 + -0.90625 Combine like terms: -1.253510695 + -0.90625 = -2.159760695 x = -2.159760695 Simplifying x = -2.159760695

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.347260695, -2.159760695}

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