16x^2+16x+4=6+3x

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Solution for 16x^2+16x+4=6+3x equation:


Simplifying
16x2 + 16x + 4 = 6 + 3x

Reorder the terms:
4 + 16x + 16x2 = 6 + 3x

Solving
4 + 16x + 16x2 = 6 + 3x

Solving for variable 'x'.

Reorder the terms:
4 + -6 + 16x + -3x + 16x2 = 6 + 3x + -6 + -3x

Combine like terms: 4 + -6 = -2
-2 + 16x + -3x + 16x2 = 6 + 3x + -6 + -3x

Combine like terms: 16x + -3x = 13x
-2 + 13x + 16x2 = 6 + 3x + -6 + -3x

Reorder the terms:
-2 + 13x + 16x2 = 6 + -6 + 3x + -3x

Combine like terms: 6 + -6 = 0
-2 + 13x + 16x2 = 0 + 3x + -3x
-2 + 13x + 16x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-2 + 13x + 16x2 = 0

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

Divide each side by '16'.
-0.125 + 0.8125x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 0.8125x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 0.8125x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 0.8125x + x2 = 0 + 0.125
0.8125x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
0.8125x + x2 = 0.125

The x term is 0.8125x.  Take half its coefficient (0.40625).
Square it (0.1650390625) and add it to both sides.

Add '0.1650390625' to each side of the equation.
0.8125x + 0.1650390625 + x2 = 0.125 + 0.1650390625

Reorder the terms:
0.1650390625 + 0.8125x + x2 = 0.125 + 0.1650390625

Combine like terms: 0.125 + 0.1650390625 = 0.2900390625
0.1650390625 + 0.8125x + x2 = 0.2900390625

Factor a perfect square on the left side:
(x + 0.40625)(x + 0.40625) = 0.2900390625

Calculate the square root of the right side: 0.538552748

Break this problem into two subproblems by setting 
(x + 0.40625) equal to 0.538552748 and -0.538552748.

Subproblem 1

x + 0.40625 = 0.538552748 Simplifying x + 0.40625 = 0.538552748 Reorder the terms: 0.40625 + x = 0.538552748 Solving 0.40625 + x = 0.538552748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.40625' to each side of the equation. 0.40625 + -0.40625 + x = 0.538552748 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + x = 0.538552748 + -0.40625 x = 0.538552748 + -0.40625 Combine like terms: 0.538552748 + -0.40625 = 0.132302748 x = 0.132302748 Simplifying x = 0.132302748

Subproblem 2

x + 0.40625 = -0.538552748 Simplifying x + 0.40625 = -0.538552748 Reorder the terms: 0.40625 + x = -0.538552748 Solving 0.40625 + x = -0.538552748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.40625' to each side of the equation. 0.40625 + -0.40625 + x = -0.538552748 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + x = -0.538552748 + -0.40625 x = -0.538552748 + -0.40625 Combine like terms: -0.538552748 + -0.40625 = -0.944802748 x = -0.944802748 Simplifying x = -0.944802748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.132302748, -0.944802748}

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