2a^2-6a-18=1

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Solution for 2a^2-6a-18=1 equation:


Simplifying
2a2 + -6a + -18 = 1

Reorder the terms:
-18 + -6a + 2a2 = 1

Solving
-18 + -6a + 2a2 = 1

Solving for variable 'a'.

Reorder the terms:
-18 + -1 + -6a + 2a2 = 1 + -1

Combine like terms: -18 + -1 = -19
-19 + -6a + 2a2 = 1 + -1

Combine like terms: 1 + -1 = 0
-19 + -6a + 2a2 = 0

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

Divide each side by '2'.
-9.5 + -3a + a2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + -3a + 9.5 + a2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + -3a + a2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + -3a + a2 = 0 + 9.5
-3a + a2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
-3a + a2 = 9.5

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = 9.5 + 2.25

Reorder the terms:
2.25 + -3a + a2 = 9.5 + 2.25

Combine like terms: 9.5 + 2.25 = 11.75
2.25 + -3a + a2 = 11.75

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 11.75

Calculate the square root of the right side: 3.4278273

Break this problem into two subproblems by setting 
(a + -1.5) equal to 3.4278273 and -3.4278273.

Subproblem 1

a + -1.5 = 3.4278273 Simplifying a + -1.5 = 3.4278273 Reorder the terms: -1.5 + a = 3.4278273 Solving -1.5 + a = 3.4278273 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 3.4278273 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 3.4278273 + 1.5 a = 3.4278273 + 1.5 Combine like terms: 3.4278273 + 1.5 = 4.9278273 a = 4.9278273 Simplifying a = 4.9278273

Subproblem 2

a + -1.5 = -3.4278273 Simplifying a + -1.5 = -3.4278273 Reorder the terms: -1.5 + a = -3.4278273 Solving -1.5 + a = -3.4278273 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -3.4278273 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -3.4278273 + 1.5 a = -3.4278273 + 1.5 Combine like terms: -3.4278273 + 1.5 = -1.9278273 a = -1.9278273 Simplifying a = -1.9278273

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.9278273, -1.9278273}

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