[5a^2-20a+20]+[3a+3]=25

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Solution for [5a^2-20a+20]+[3a+3]=25 equation:


Simplifying
[5a2 + -20a + 20] + [3a + 3] = 25

Reorder the terms:
[20 + -20a + 5a2] + [3a + 3] = 25

Remove brackets around [20 + -20a + 5a2]
20 + -20a + 5a2 + [3a + 3] = 25

Reorder the terms:
20 + -20a + 5a2 + [3 + 3a] = 25

Remove brackets around [3 + 3a]
20 + -20a + 5a2 + 3 + 3a = 25

Reorder the terms:
20 + 3 + -20a + 3a + 5a2 = 25

Combine like terms: 20 + 3 = 23
23 + -20a + 3a + 5a2 = 25

Combine like terms: -20a + 3a = -17a
23 + -17a + 5a2 = 25

Solving
23 + -17a + 5a2 = 25

Solving for variable 'a'.

Reorder the terms:
23 + -25 + -17a + 5a2 = 25 + -25

Combine like terms: 23 + -25 = -2
-2 + -17a + 5a2 = 25 + -25

Combine like terms: 25 + -25 = 0
-2 + -17a + 5a2 = 0

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

Divide each side by '5'.
-0.4 + -3.4a + a2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -3.4a + 0.4 + a2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -3.4a + a2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -3.4a + a2 = 0 + 0.4
-3.4a + a2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-3.4a + a2 = 0.4

The a term is -3.4a.  Take half its coefficient (-1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
-3.4a + 2.89 + a2 = 0.4 + 2.89

Reorder the terms:
2.89 + -3.4a + a2 = 0.4 + 2.89

Combine like terms: 0.4 + 2.89 = 3.29
2.89 + -3.4a + a2 = 3.29

Factor a perfect square on the left side:
(a + -1.7)(a + -1.7) = 3.29

Calculate the square root of the right side: 1.813835715

Break this problem into two subproblems by setting 
(a + -1.7) equal to 1.813835715 and -1.813835715.

Subproblem 1

a + -1.7 = 1.813835715 Simplifying a + -1.7 = 1.813835715 Reorder the terms: -1.7 + a = 1.813835715 Solving -1.7 + a = 1.813835715 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + a = 1.813835715 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + a = 1.813835715 + 1.7 a = 1.813835715 + 1.7 Combine like terms: 1.813835715 + 1.7 = 3.513835715 a = 3.513835715 Simplifying a = 3.513835715

Subproblem 2

a + -1.7 = -1.813835715 Simplifying a + -1.7 = -1.813835715 Reorder the terms: -1.7 + a = -1.813835715 Solving -1.7 + a = -1.813835715 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + a = -1.813835715 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + a = -1.813835715 + 1.7 a = -1.813835715 + 1.7 Combine like terms: -1.813835715 + 1.7 = -0.113835715 a = -0.113835715 Simplifying a = -0.113835715

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.513835715, -0.113835715}

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