2a^2-11a-42=0

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Solution for 2a^2-11a-42=0 equation:


Simplifying
2a2 + -11a + -42 = 0

Reorder the terms:
-42 + -11a + 2a2 = 0

Solving
-42 + -11a + 2a2 = 0

Solving for variable 'a'.

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

Divide each side by '2'.
-21 + -5.5a + a2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -5.5a + 21 + a2 = 0 + 21

Reorder the terms:
-21 + 21 + -5.5a + a2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -5.5a + a2 = 0 + 21
-5.5a + a2 = 0 + 21

Combine like terms: 0 + 21 = 21
-5.5a + a2 = 21

The a term is -5.5a.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5a + 7.5625 + a2 = 21 + 7.5625

Reorder the terms:
7.5625 + -5.5a + a2 = 21 + 7.5625

Combine like terms: 21 + 7.5625 = 28.5625
7.5625 + -5.5a + a2 = 28.5625

Factor a perfect square on the left side:
(a + -2.75)(a + -2.75) = 28.5625

Calculate the square root of the right side: 5.344389582

Break this problem into two subproblems by setting 
(a + -2.75) equal to 5.344389582 and -5.344389582.

Subproblem 1

a + -2.75 = 5.344389582 Simplifying a + -2.75 = 5.344389582 Reorder the terms: -2.75 + a = 5.344389582 Solving -2.75 + a = 5.344389582 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + a = 5.344389582 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = 5.344389582 + 2.75 a = 5.344389582 + 2.75 Combine like terms: 5.344389582 + 2.75 = 8.094389582 a = 8.094389582 Simplifying a = 8.094389582

Subproblem 2

a + -2.75 = -5.344389582 Simplifying a + -2.75 = -5.344389582 Reorder the terms: -2.75 + a = -5.344389582 Solving -2.75 + a = -5.344389582 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + a = -5.344389582 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = -5.344389582 + 2.75 a = -5.344389582 + 2.75 Combine like terms: -5.344389582 + 2.75 = -2.594389582 a = -2.594389582 Simplifying a = -2.594389582

Solution

The solution to the problem is based on the solutions from the subproblems. a = {8.094389582, -2.594389582}

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