a^2+5a-40=0

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Solution for a^2+5a-40=0 equation:


Simplifying
a2 + 5a + -40 = 0

Reorder the terms:
-40 + 5a + a2 = 0

Solving
-40 + 5a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 5a + 40 + a2 = 0 + 40

Reorder the terms:
-40 + 40 + 5a + a2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 5a + a2 = 0 + 40
5a + a2 = 0 + 40

Combine like terms: 0 + 40 = 40
5a + a2 = 40

The a term is 5a.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5a + 6.25 + a2 = 40 + 6.25

Reorder the terms:
6.25 + 5a + a2 = 40 + 6.25

Combine like terms: 40 + 6.25 = 46.25
6.25 + 5a + a2 = 46.25

Factor a perfect square on the left side:
(a + 2.5)(a + 2.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(a + 2.5) equal to 6.800735254 and -6.800735254.

Subproblem 1

a + 2.5 = 6.800735254 Simplifying a + 2.5 = 6.800735254 Reorder the terms: 2.5 + a = 6.800735254 Solving 2.5 + a = 6.800735254 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = 6.800735254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 6.800735254 + -2.5 a = 6.800735254 + -2.5 Combine like terms: 6.800735254 + -2.5 = 4.300735254 a = 4.300735254 Simplifying a = 4.300735254

Subproblem 2

a + 2.5 = -6.800735254 Simplifying a + 2.5 = -6.800735254 Reorder the terms: 2.5 + a = -6.800735254 Solving 2.5 + a = -6.800735254 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = -6.800735254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -6.800735254 + -2.5 a = -6.800735254 + -2.5 Combine like terms: -6.800735254 + -2.5 = -9.300735254 a = -9.300735254 Simplifying a = -9.300735254

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.300735254, -9.300735254}

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