a^2+14a-60=0

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Solution for a^2+14a-60=0 equation:


Simplifying
a2 + 14a + -60 = 0

Reorder the terms:
-60 + 14a + a2 = 0

Solving
-60 + 14a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 14a + 60 + a2 = 0 + 60

Reorder the terms:
-60 + 60 + 14a + a2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 14a + a2 = 0 + 60
14a + a2 = 0 + 60

Combine like terms: 0 + 60 = 60
14a + a2 = 60

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 = 60 + 49

Reorder the terms:
49 + 14a + a2 = 60 + 49

Combine like terms: 60 + 49 = 109
49 + 14a + a2 = 109

Factor a perfect square on the left side:
(a + 7)(a + 7) = 109

Calculate the square root of the right side: 10.440306509

Break this problem into two subproblems by setting 
(a + 7) equal to 10.440306509 and -10.440306509.

Subproblem 1

a + 7 = 10.440306509 Simplifying a + 7 = 10.440306509 Reorder the terms: 7 + a = 10.440306509 Solving 7 + a = 10.440306509 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 = 10.440306509 + -7 Combine like terms: 7 + -7 = 0 0 + a = 10.440306509 + -7 a = 10.440306509 + -7 Combine like terms: 10.440306509 + -7 = 3.440306509 a = 3.440306509 Simplifying a = 3.440306509

Subproblem 2

a + 7 = -10.440306509 Simplifying a + 7 = -10.440306509 Reorder the terms: 7 + a = -10.440306509 Solving 7 + a = -10.440306509 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 = -10.440306509 + -7 Combine like terms: 7 + -7 = 0 0 + a = -10.440306509 + -7 a = -10.440306509 + -7 Combine like terms: -10.440306509 + -7 = -17.440306509 a = -17.440306509 Simplifying a = -17.440306509

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.440306509, -17.440306509}

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