a^2+3a-63=0

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Solution for a^2+3a-63=0 equation:


Simplifying
a2 + 3a + -63 = 0

Reorder the terms:
-63 + 3a + a2 = 0

Solving
-63 + 3a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '63' to each side of the equation.
-63 + 3a + 63 + a2 = 0 + 63

Reorder the terms:
-63 + 63 + 3a + a2 = 0 + 63

Combine like terms: -63 + 63 = 0
0 + 3a + a2 = 0 + 63
3a + a2 = 0 + 63

Combine like terms: 0 + 63 = 63
3a + a2 = 63

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 = 63 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 63 + 2.25

Combine like terms: 63 + 2.25 = 65.25
2.25 + 3a + a2 = 65.25

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 65.25

Calculate the square root of the right side: 8.077747211

Break this problem into two subproblems by setting 
(a + 1.5) equal to 8.077747211 and -8.077747211.

Subproblem 1

a + 1.5 = 8.077747211 Simplifying a + 1.5 = 8.077747211 Reorder the terms: 1.5 + a = 8.077747211 Solving 1.5 + a = 8.077747211 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 = 8.077747211 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 8.077747211 + -1.5 a = 8.077747211 + -1.5 Combine like terms: 8.077747211 + -1.5 = 6.577747211 a = 6.577747211 Simplifying a = 6.577747211

Subproblem 2

a + 1.5 = -8.077747211 Simplifying a + 1.5 = -8.077747211 Reorder the terms: 1.5 + a = -8.077747211 Solving 1.5 + a = -8.077747211 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 = -8.077747211 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -8.077747211 + -1.5 a = -8.077747211 + -1.5 Combine like terms: -8.077747211 + -1.5 = -9.577747211 a = -9.577747211 Simplifying a = -9.577747211

Solution

The solution to the problem is based on the solutions from the subproblems. a = {6.577747211, -9.577747211}

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