3a^2+18a-7=0

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Solution for 3a^2+18a-7=0 equation:


Simplifying
3a2 + 18a + -7 = 0

Reorder the terms:
-7 + 18a + 3a2 = 0

Solving
-7 + 18a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
-2.333333333 + 6a + a2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 6a + 2.333333333 + a2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 6a + a2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 6a + a2 = 0 + 2.333333333
6a + a2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
6a + a2 = 2.333333333

The a term is 6a.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6a + 9 + a2 = 2.333333333 + 9

Reorder the terms:
9 + 6a + a2 = 2.333333333 + 9

Combine like terms: 2.333333333 + 9 = 11.333333333
9 + 6a + a2 = 11.333333333

Factor a perfect square on the left side:
(a + 3)(a + 3) = 11.333333333

Calculate the square root of the right side: 3.366501646

Break this problem into two subproblems by setting 
(a + 3) equal to 3.366501646 and -3.366501646.

Subproblem 1

a + 3 = 3.366501646 Simplifying a + 3 = 3.366501646 Reorder the terms: 3 + a = 3.366501646 Solving 3 + a = 3.366501646 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 3.366501646 + -3 Combine like terms: 3 + -3 = 0 0 + a = 3.366501646 + -3 a = 3.366501646 + -3 Combine like terms: 3.366501646 + -3 = 0.366501646 a = 0.366501646 Simplifying a = 0.366501646

Subproblem 2

a + 3 = -3.366501646 Simplifying a + 3 = -3.366501646 Reorder the terms: 3 + a = -3.366501646 Solving 3 + a = -3.366501646 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -3.366501646 + -3 Combine like terms: 3 + -3 = 0 0 + a = -3.366501646 + -3 a = -3.366501646 + -3 Combine like terms: -3.366501646 + -3 = -6.366501646 a = -6.366501646 Simplifying a = -6.366501646

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.366501646, -6.366501646}

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