a^2+14a-5=0

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Solution for a^2+14a-5=0 equation:


Simplifying
a2 + 14a + -5 = 0

Reorder the terms:
-5 + 14a + a2 = 0

Solving
-5 + 14a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 14a + 5 + a2 = 0 + 5

Reorder the terms:
-5 + 5 + 14a + a2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 14a + a2 = 0 + 5
14a + a2 = 0 + 5

Combine like terms: 0 + 5 = 5
14a + a2 = 5

The a term is 14a.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14a + 49 + a2 = 5 + 49

Reorder the terms:
49 + 14a + a2 = 5 + 49

Combine like terms: 5 + 49 = 54
49 + 14a + a2 = 54

Factor a perfect square on the left side:
(a + 7)(a + 7) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(a + 7) equal to 7.348469228 and -7.348469228.

Subproblem 1

a + 7 = 7.348469228 Simplifying a + 7 = 7.348469228 Reorder the terms: 7 + a = 7.348469228 Solving 7 + a = 7.348469228 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = 7.348469228 + -7 Combine like terms: 7 + -7 = 0 0 + a = 7.348469228 + -7 a = 7.348469228 + -7 Combine like terms: 7.348469228 + -7 = 0.348469228 a = 0.348469228 Simplifying a = 0.348469228

Subproblem 2

a + 7 = -7.348469228 Simplifying a + 7 = -7.348469228 Reorder the terms: 7 + a = -7.348469228 Solving 7 + a = -7.348469228 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = -7.348469228 + -7 Combine like terms: 7 + -7 = 0 0 + a = -7.348469228 + -7 a = -7.348469228 + -7 Combine like terms: -7.348469228 + -7 = -14.348469228 a = -14.348469228 Simplifying a = -14.348469228

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.348469228, -14.348469228}

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