(2X^2-13X+7)-(1+12X)=

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Solution for (2X^2-13X+7)-(1+12X)= equation:


Simplifying
(2X2 + -13X + 7) + -1(1 + 12X) = 0

Reorder the terms:
(7 + -13X + 2X2) + -1(1 + 12X) = 0

Remove parenthesis around (7 + -13X + 2X2)
7 + -13X + 2X2 + -1(1 + 12X) = 0
7 + -13X + 2X2 + (1 * -1 + 12X * -1) = 0
7 + -13X + 2X2 + (-1 + -12X) = 0

Reorder the terms:
7 + -1 + -13X + -12X + 2X2 = 0

Combine like terms: 7 + -1 = 6
6 + -13X + -12X + 2X2 = 0

Combine like terms: -13X + -12X = -25X
6 + -25X + 2X2 = 0

Solving
6 + -25X + 2X2 = 0

Solving for variable 'X'.

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

Divide each side by '2'.
3 + -12.5X + X2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -12.5X + -3 + X2 = 0 + -3

Reorder the terms:
3 + -3 + -12.5X + X2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -12.5X + X2 = 0 + -3
-12.5X + X2 = 0 + -3

Combine like terms: 0 + -3 = -3
-12.5X + X2 = -3

The X term is -12.5X.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5X + 39.0625 + X2 = -3 + 39.0625

Reorder the terms:
39.0625 + -12.5X + X2 = -3 + 39.0625

Combine like terms: -3 + 39.0625 = 36.0625
39.0625 + -12.5X + X2 = 36.0625

Factor a perfect square on the left side:
(X + -6.25)(X + -6.25) = 36.0625

Calculate the square root of the right side: 6.005206075

Break this problem into two subproblems by setting 
(X + -6.25) equal to 6.005206075 and -6.005206075.

Subproblem 1

X + -6.25 = 6.005206075 Simplifying X + -6.25 = 6.005206075 Reorder the terms: -6.25 + X = 6.005206075 Solving -6.25 + X = 6.005206075 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + X = 6.005206075 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + X = 6.005206075 + 6.25 X = 6.005206075 + 6.25 Combine like terms: 6.005206075 + 6.25 = 12.255206075 X = 12.255206075 Simplifying X = 12.255206075

Subproblem 2

X + -6.25 = -6.005206075 Simplifying X + -6.25 = -6.005206075 Reorder the terms: -6.25 + X = -6.005206075 Solving -6.25 + X = -6.005206075 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + X = -6.005206075 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + X = -6.005206075 + 6.25 X = -6.005206075 + 6.25 Combine like terms: -6.005206075 + 6.25 = 0.244793925 X = 0.244793925 Simplifying X = 0.244793925

Solution

The solution to the problem is based on the solutions from the subproblems. X = {12.255206075, 0.244793925}

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