4X*4X=13X+12

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Solution for 4X*4X=13X+12 equation:


Simplifying
4X * 4X = 13X + 12

Reorder the terms for easier multiplication:
4 * 4X * X = 13X + 12

Multiply 4 * 4
16X * X = 13X + 12

Multiply X * X
16X2 = 13X + 12

Reorder the terms:
16X2 = 12 + 13X

Solving
16X2 = 12 + 13X

Solving for variable 'X'.

Reorder the terms:
-12 + -13X + 16X2 = 12 + 13X + -12 + -13X

Reorder the terms:
-12 + -13X + 16X2 = 12 + -12 + 13X + -13X

Combine like terms: 12 + -12 = 0
-12 + -13X + 16X2 = 0 + 13X + -13X
-12 + -13X + 16X2 = 13X + -13X

Combine like terms: 13X + -13X = 0
-12 + -13X + 16X2 = 0

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

Divide each side by '16'.
-0.75 + -0.8125X + X2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -0.8125X + 0.75 + X2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -0.8125X + X2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -0.8125X + X2 = 0 + 0.75
-0.8125X + X2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-0.8125X + X2 = 0.75

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 = 0.75 + 0.1650390625

Reorder the terms:
0.1650390625 + -0.8125X + X2 = 0.75 + 0.1650390625

Combine like terms: 0.75 + 0.1650390625 = 0.9150390625
0.1650390625 + -0.8125X + X2 = 0.9150390625

Factor a perfect square on the left side:
(X + -0.40625)(X + -0.40625) = 0.9150390625

Calculate the square root of the right side: 0.956576742

Break this problem into two subproblems by setting 
(X + -0.40625) equal to 0.956576742 and -0.956576742.

Subproblem 1

X + -0.40625 = 0.956576742 Simplifying X + -0.40625 = 0.956576742 Reorder the terms: -0.40625 + X = 0.956576742 Solving -0.40625 + X = 0.956576742 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 = 0.956576742 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + X = 0.956576742 + 0.40625 X = 0.956576742 + 0.40625 Combine like terms: 0.956576742 + 0.40625 = 1.362826742 X = 1.362826742 Simplifying X = 1.362826742

Subproblem 2

X + -0.40625 = -0.956576742 Simplifying X + -0.40625 = -0.956576742 Reorder the terms: -0.40625 + X = -0.956576742 Solving -0.40625 + X = -0.956576742 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 = -0.956576742 + 0.40625 Combine like terms: -0.40625 + 0.40625 = 0.00000 0.00000 + X = -0.956576742 + 0.40625 X = -0.956576742 + 0.40625 Combine like terms: -0.956576742 + 0.40625 = -0.550326742 X = -0.550326742 Simplifying X = -0.550326742

Solution

The solution to the problem is based on the solutions from the subproblems. X = {1.362826742, -0.550326742}

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