2x^2-21x+12=0

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Solution for 2x^2-21x+12=0 equation:


Simplifying
2x2 + -21x + 12 = 0

Reorder the terms:
12 + -21x + 2x2 = 0

Solving
12 + -21x + 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'.
6 + -10.5x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -10.5x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -10.5x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -10.5x + x2 = 0 + -6
-10.5x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-10.5x + x2 = -6

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = -6 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = -6 + 27.5625

Combine like terms: -6 + 27.5625 = 21.5625
27.5625 + -10.5x + x2 = 21.5625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 21.5625

Calculate the square root of the right side: 4.643543905

Break this problem into two subproblems by setting 
(x + -5.25) equal to 4.643543905 and -4.643543905.

Subproblem 1

x + -5.25 = 4.643543905 Simplifying x + -5.25 = 4.643543905 Reorder the terms: -5.25 + x = 4.643543905 Solving -5.25 + x = 4.643543905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 4.643543905 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 4.643543905 + 5.25 x = 4.643543905 + 5.25 Combine like terms: 4.643543905 + 5.25 = 9.893543905 x = 9.893543905 Simplifying x = 9.893543905

Subproblem 2

x + -5.25 = -4.643543905 Simplifying x + -5.25 = -4.643543905 Reorder the terms: -5.25 + x = -4.643543905 Solving -5.25 + x = -4.643543905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -4.643543905 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -4.643543905 + 5.25 x = -4.643543905 + 5.25 Combine like terms: -4.643543905 + 5.25 = 0.606456095 x = 0.606456095 Simplifying x = 0.606456095

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.893543905, 0.606456095}

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