3a^2+6a=7

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Solution for 3a^2+6a=7 equation:


Simplifying
3a2 + 6a = 7

Reorder the terms:
6a + 3a2 = 7

Solving
6a + 3a2 = 7

Solving for variable 'a'.

Reorder the terms:
-7 + 6a + 3a2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 6a + 3a2 = 0

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

Divide each side by '3'.
-2.333333333 + 2a + a2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 2a + 2.333333333 + a2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 2a + a2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 2a + a2 = 0 + 2.333333333
2a + a2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
2a + a2 = 2.333333333

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 2.333333333 + 1

Reorder the terms:
1 + 2a + a2 = 2.333333333 + 1

Combine like terms: 2.333333333 + 1 = 3.333333333
1 + 2a + a2 = 3.333333333

Factor a perfect square on the left side:
(a + 1)(a + 1) = 3.333333333

Calculate the square root of the right side: 1.825741858

Break this problem into two subproblems by setting 
(a + 1) equal to 1.825741858 and -1.825741858.

Subproblem 1

a + 1 = 1.825741858 Simplifying a + 1 = 1.825741858 Reorder the terms: 1 + a = 1.825741858 Solving 1 + a = 1.825741858 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 1.825741858 + -1 Combine like terms: 1 + -1 = 0 0 + a = 1.825741858 + -1 a = 1.825741858 + -1 Combine like terms: 1.825741858 + -1 = 0.825741858 a = 0.825741858 Simplifying a = 0.825741858

Subproblem 2

a + 1 = -1.825741858 Simplifying a + 1 = -1.825741858 Reorder the terms: 1 + a = -1.825741858 Solving 1 + a = -1.825741858 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -1.825741858 + -1 Combine like terms: 1 + -1 = 0 0 + a = -1.825741858 + -1 a = -1.825741858 + -1 Combine like terms: -1.825741858 + -1 = -2.825741858 a = -2.825741858 Simplifying a = -2.825741858

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.825741858, -2.825741858}

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