a^2+4a-40=

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Solution for a^2+4a-40= equation:


Simplifying
a2 + 4a + -40 = 0

Reorder the terms:
-40 + 4a + a2 = 0

Solving
-40 + 4a + 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 + 4a + 40 + a2 = 0 + 40

Reorder the terms:
-40 + 40 + 4a + a2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 4a + a2 = 0 + 40
4a + a2 = 0 + 40

Combine like terms: 0 + 40 = 40
4a + a2 = 40

The a term is 4a.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4a + 4 + a2 = 40 + 4

Reorder the terms:
4 + 4a + a2 = 40 + 4

Combine like terms: 40 + 4 = 44
4 + 4a + a2 = 44

Factor a perfect square on the left side:
(a + 2)(a + 2) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(a + 2) equal to 6.633249581 and -6.633249581.

Subproblem 1

a + 2 = 6.633249581 Simplifying a + 2 = 6.633249581 Reorder the terms: 2 + a = 6.633249581 Solving 2 + a = 6.633249581 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 6.633249581 + -2 Combine like terms: 2 + -2 = 0 0 + a = 6.633249581 + -2 a = 6.633249581 + -2 Combine like terms: 6.633249581 + -2 = 4.633249581 a = 4.633249581 Simplifying a = 4.633249581

Subproblem 2

a + 2 = -6.633249581 Simplifying a + 2 = -6.633249581 Reorder the terms: 2 + a = -6.633249581 Solving 2 + a = -6.633249581 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -6.633249581 + -2 Combine like terms: 2 + -2 = 0 0 + a = -6.633249581 + -2 a = -6.633249581 + -2 Combine like terms: -6.633249581 + -2 = -8.633249581 a = -8.633249581 Simplifying a = -8.633249581

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.633249581, -8.633249581}

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