a^2+11a-51=0

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Solution for a^2+11a-51=0 equation:


Simplifying
a2 + 11a + -51 = 0

Reorder the terms:
-51 + 11a + a2 = 0

Solving
-51 + 11a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + 11a + 51 + a2 = 0 + 51

Reorder the terms:
-51 + 51 + 11a + a2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + 11a + a2 = 0 + 51
11a + a2 = 0 + 51

Combine like terms: 0 + 51 = 51
11a + a2 = 51

The a term is 11a.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11a + 30.25 + a2 = 51 + 30.25

Reorder the terms:
30.25 + 11a + a2 = 51 + 30.25

Combine like terms: 51 + 30.25 = 81.25
30.25 + 11a + a2 = 81.25

Factor a perfect square on the left side:
(a + 5.5)(a + 5.5) = 81.25

Calculate the square root of the right side: 9.013878189

Break this problem into two subproblems by setting 
(a + 5.5) equal to 9.013878189 and -9.013878189.

Subproblem 1

a + 5.5 = 9.013878189 Simplifying a + 5.5 = 9.013878189 Reorder the terms: 5.5 + a = 9.013878189 Solving 5.5 + a = 9.013878189 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + a = 9.013878189 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = 9.013878189 + -5.5 a = 9.013878189 + -5.5 Combine like terms: 9.013878189 + -5.5 = 3.513878189 a = 3.513878189 Simplifying a = 3.513878189

Subproblem 2

a + 5.5 = -9.013878189 Simplifying a + 5.5 = -9.013878189 Reorder the terms: 5.5 + a = -9.013878189 Solving 5.5 + a = -9.013878189 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + a = -9.013878189 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = -9.013878189 + -5.5 a = -9.013878189 + -5.5 Combine like terms: -9.013878189 + -5.5 = -14.513878189 a = -14.513878189 Simplifying a = -14.513878189

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.513878189, -14.513878189}

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