a^2+3a-32=0

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Solution for a^2+3a-32=0 equation:


Simplifying
a2 + 3a + -32 = 0

Reorder the terms:
-32 + 3a + a2 = 0

Solving
-32 + 3a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 3a + 32 + a2 = 0 + 32

Reorder the terms:
-32 + 32 + 3a + a2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 3a + a2 = 0 + 32
3a + a2 = 0 + 32

Combine like terms: 0 + 32 = 32
3a + a2 = 32

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 = 32 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 32 + 2.25

Combine like terms: 32 + 2.25 = 34.25
2.25 + 3a + a2 = 34.25

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(a + 1.5) equal to 5.852349955 and -5.852349955.

Subproblem 1

a + 1.5 = 5.852349955 Simplifying a + 1.5 = 5.852349955 Reorder the terms: 1.5 + a = 5.852349955 Solving 1.5 + a = 5.852349955 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 = 5.852349955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 5.852349955 + -1.5 a = 5.852349955 + -1.5 Combine like terms: 5.852349955 + -1.5 = 4.352349955 a = 4.352349955 Simplifying a = 4.352349955

Subproblem 2

a + 1.5 = -5.852349955 Simplifying a + 1.5 = -5.852349955 Reorder the terms: 1.5 + a = -5.852349955 Solving 1.5 + a = -5.852349955 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 = -5.852349955 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -5.852349955 + -1.5 a = -5.852349955 + -1.5 Combine like terms: -5.852349955 + -1.5 = -7.352349955 a = -7.352349955 Simplifying a = -7.352349955

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.352349955, -7.352349955}

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