3a^2+6a-18=5

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Solution for 3a^2+6a-18=5 equation:


Simplifying
3a2 + 6a + -18 = 5

Reorder the terms:
-18 + 6a + 3a2 = 5

Solving
-18 + 6a + 3a2 = 5

Solving for variable 'a'.

Reorder the terms:
-18 + -5 + 6a + 3a2 = 5 + -5

Combine like terms: -18 + -5 = -23
-23 + 6a + 3a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-23 + 6a + 3a2 = 0

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

Divide each side by '3'.
-7.666666667 + 2a + a2 = 0

Move the constant term to the right:

Add '7.666666667' to each side of the equation.
-7.666666667 + 2a + 7.666666667 + a2 = 0 + 7.666666667

Reorder the terms:
-7.666666667 + 7.666666667 + 2a + a2 = 0 + 7.666666667

Combine like terms: -7.666666667 + 7.666666667 = 0.000000000
0.000000000 + 2a + a2 = 0 + 7.666666667
2a + a2 = 0 + 7.666666667

Combine like terms: 0 + 7.666666667 = 7.666666667
2a + a2 = 7.666666667

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 = 7.666666667 + 1

Reorder the terms:
1 + 2a + a2 = 7.666666667 + 1

Combine like terms: 7.666666667 + 1 = 8.666666667
1 + 2a + a2 = 8.666666667

Factor a perfect square on the left side:
(a + 1)(a + 1) = 8.666666667

Calculate the square root of the right side: 2.943920289

Break this problem into two subproblems by setting 
(a + 1) equal to 2.943920289 and -2.943920289.

Subproblem 1

a + 1 = 2.943920289 Simplifying a + 1 = 2.943920289 Reorder the terms: 1 + a = 2.943920289 Solving 1 + a = 2.943920289 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 = 2.943920289 + -1 Combine like terms: 1 + -1 = 0 0 + a = 2.943920289 + -1 a = 2.943920289 + -1 Combine like terms: 2.943920289 + -1 = 1.943920289 a = 1.943920289 Simplifying a = 1.943920289

Subproblem 2

a + 1 = -2.943920289 Simplifying a + 1 = -2.943920289 Reorder the terms: 1 + a = -2.943920289 Solving 1 + a = -2.943920289 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 = -2.943920289 + -1 Combine like terms: 1 + -1 = 0 0 + a = -2.943920289 + -1 a = -2.943920289 + -1 Combine like terms: -2.943920289 + -1 = -3.943920289 a = -3.943920289 Simplifying a = -3.943920289

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.943920289, -3.943920289}

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