16x^2=4x^2+3x+1

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Solution for 16x^2=4x^2+3x+1 equation:


Simplifying
16x2 = 4x2 + 3x + 1

Reorder the terms:
16x2 = 1 + 3x + 4x2

Solving
16x2 = 1 + 3x + 4x2

Solving for variable 'x'.

Reorder the terms:
-1 + -3x + 16x2 + -4x2 = 1 + 3x + 4x2 + -1 + -3x + -4x2

Combine like terms: 16x2 + -4x2 = 12x2
-1 + -3x + 12x2 = 1 + 3x + 4x2 + -1 + -3x + -4x2

Reorder the terms:
-1 + -3x + 12x2 = 1 + -1 + 3x + -3x + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
-1 + -3x + 12x2 = 0 + 3x + -3x + 4x2 + -4x2
-1 + -3x + 12x2 = 3x + -3x + 4x2 + -4x2

Combine like terms: 3x + -3x = 0
-1 + -3x + 12x2 = 0 + 4x2 + -4x2
-1 + -3x + 12x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-1 + -3x + 12x2 = 0

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

Divide each side by '12'.
-0.08333333333 + -0.25x + x2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + -0.25x + 0.08333333333 + x2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + -0.25x + x2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + -0.25x + x2 = 0 + 0.08333333333
-0.25x + x2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
-0.25x + x2 = 0.08333333333

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = 0.08333333333 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = 0.08333333333 + 0.015625

Combine like terms: 0.08333333333 + 0.015625 = 0.09895833333
0.015625 + -0.25x + x2 = 0.09895833333

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = 0.09895833333

Calculate the square root of the right side: 0.314576435

Break this problem into two subproblems by setting 
(x + -0.125) equal to 0.314576435 and -0.314576435.

Subproblem 1

x + -0.125 = 0.314576435 Simplifying x + -0.125 = 0.314576435 Reorder the terms: -0.125 + x = 0.314576435 Solving -0.125 + x = 0.314576435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.314576435 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.314576435 + 0.125 x = 0.314576435 + 0.125 Combine like terms: 0.314576435 + 0.125 = 0.439576435 x = 0.439576435 Simplifying x = 0.439576435

Subproblem 2

x + -0.125 = -0.314576435 Simplifying x + -0.125 = -0.314576435 Reorder the terms: -0.125 + x = -0.314576435 Solving -0.125 + x = -0.314576435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.314576435 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.314576435 + 0.125 x = -0.314576435 + 0.125 Combine like terms: -0.314576435 + 0.125 = -0.189576435 x = -0.189576435 Simplifying x = -0.189576435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.439576435, -0.189576435}

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