2x^2+21x-54=0

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Solution for 2x^2+21x-54=0 equation:


Simplifying
2x2 + 21x + -54 = 0

Reorder the terms:
-54 + 21x + 2x2 = 0

Solving
-54 + 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'.
-27 + 10.5x + x2 = 0

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 10.5x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + 10.5x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 10.5x + x2 = 0 + 27
10.5x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
10.5x + x2 = 27

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 = 27 + 27.5625

Reorder the terms:
27.5625 + 10.5x + x2 = 27 + 27.5625

Combine like terms: 27 + 27.5625 = 54.5625
27.5625 + 10.5x + x2 = 54.5625

Factor a perfect square on the left side:
(x + 5.25)(x + 5.25) = 54.5625

Calculate the square root of the right side: 7.386643351

Break this problem into two subproblems by setting 
(x + 5.25) equal to 7.386643351 and -7.386643351.

Subproblem 1

x + 5.25 = 7.386643351 Simplifying x + 5.25 = 7.386643351 Reorder the terms: 5.25 + x = 7.386643351 Solving 5.25 + x = 7.386643351 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 = 7.386643351 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 7.386643351 + -5.25 x = 7.386643351 + -5.25 Combine like terms: 7.386643351 + -5.25 = 2.136643351 x = 2.136643351 Simplifying x = 2.136643351

Subproblem 2

x + 5.25 = -7.386643351 Simplifying x + 5.25 = -7.386643351 Reorder the terms: 5.25 + x = -7.386643351 Solving 5.25 + x = -7.386643351 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 = -7.386643351 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -7.386643351 + -5.25 x = -7.386643351 + -5.25 Combine like terms: -7.386643351 + -5.25 = -12.636643351 x = -12.636643351 Simplifying x = -12.636643351

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.136643351, -12.636643351}

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