7a^2+49a+60=0

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Solution for 7a^2+49a+60=0 equation:


Simplifying
7a2 + 49a + 60 = 0

Reorder the terms:
60 + 49a + 7a2 = 0

Solving
60 + 49a + 7a2 = 0

Solving for variable 'a'.

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

Divide each side by '7'.
8.571428571 + 7a + a2 = 0

Move the constant term to the right:

Add '-8.571428571' to each side of the equation.
8.571428571 + 7a + -8.571428571 + a2 = 0 + -8.571428571

Reorder the terms:
8.571428571 + -8.571428571 + 7a + a2 = 0 + -8.571428571

Combine like terms: 8.571428571 + -8.571428571 = 0.000000000
0.000000000 + 7a + a2 = 0 + -8.571428571
7a + a2 = 0 + -8.571428571

Combine like terms: 0 + -8.571428571 = -8.571428571
7a + a2 = -8.571428571

The a term is 7a.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7a + 12.25 + a2 = -8.571428571 + 12.25

Reorder the terms:
12.25 + 7a + a2 = -8.571428571 + 12.25

Combine like terms: -8.571428571 + 12.25 = 3.678571429
12.25 + 7a + a2 = 3.678571429

Factor a perfect square on the left side:
(a + 3.5)(a + 3.5) = 3.678571429

Calculate the square root of the right side: 1.917960226

Break this problem into two subproblems by setting 
(a + 3.5) equal to 1.917960226 and -1.917960226.

Subproblem 1

a + 3.5 = 1.917960226 Simplifying a + 3.5 = 1.917960226 Reorder the terms: 3.5 + a = 1.917960226 Solving 3.5 + a = 1.917960226 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + a = 1.917960226 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = 1.917960226 + -3.5 a = 1.917960226 + -3.5 Combine like terms: 1.917960226 + -3.5 = -1.582039774 a = -1.582039774 Simplifying a = -1.582039774

Subproblem 2

a + 3.5 = -1.917960226 Simplifying a + 3.5 = -1.917960226 Reorder the terms: 3.5 + a = -1.917960226 Solving 3.5 + a = -1.917960226 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + a = -1.917960226 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = -1.917960226 + -3.5 a = -1.917960226 + -3.5 Combine like terms: -1.917960226 + -3.5 = -5.417960226 a = -5.417960226 Simplifying a = -5.417960226

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-1.582039774, -5.417960226}

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