4a^2-12a-153=0

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Solution for 4a^2-12a-153=0 equation:


Simplifying
4a2 + -12a + -153 = 0

Reorder the terms:
-153 + -12a + 4a2 = 0

Solving
-153 + -12a + 4a2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
-38.25 + -3a + a2 = 0

Move the constant term to the right:

Add '38.25' to each side of the equation.
-38.25 + -3a + 38.25 + a2 = 0 + 38.25

Reorder the terms:
-38.25 + 38.25 + -3a + a2 = 0 + 38.25

Combine like terms: -38.25 + 38.25 = 0.00
0.00 + -3a + a2 = 0 + 38.25
-3a + a2 = 0 + 38.25

Combine like terms: 0 + 38.25 = 38.25
-3a + a2 = 38.25

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 = 38.25 + 2.25

Reorder the terms:
2.25 + -3a + a2 = 38.25 + 2.25

Combine like terms: 38.25 + 2.25 = 40.5
2.25 + -3a + a2 = 40.5

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 40.5

Calculate the square root of the right side: 6.363961031

Break this problem into two subproblems by setting 
(a + -1.5) equal to 6.363961031 and -6.363961031.

Subproblem 1

a + -1.5 = 6.363961031 Simplifying a + -1.5 = 6.363961031 Reorder the terms: -1.5 + a = 6.363961031 Solving -1.5 + a = 6.363961031 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 = 6.363961031 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 6.363961031 + 1.5 a = 6.363961031 + 1.5 Combine like terms: 6.363961031 + 1.5 = 7.863961031 a = 7.863961031 Simplifying a = 7.863961031

Subproblem 2

a + -1.5 = -6.363961031 Simplifying a + -1.5 = -6.363961031 Reorder the terms: -1.5 + a = -6.363961031 Solving -1.5 + a = -6.363961031 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 = -6.363961031 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -6.363961031 + 1.5 a = -6.363961031 + 1.5 Combine like terms: -6.363961031 + 1.5 = -4.863961031 a = -4.863961031 Simplifying a = -4.863961031

Solution

The solution to the problem is based on the solutions from the subproblems. a = {7.863961031, -4.863961031}

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