5(a-2)(a-2)=70

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Solution for 5(a-2)(a-2)=70 equation: 


Simplifying
5(a + -2)(a + -2) = 70

Reorder the terms:
5(-2 + a)(a + -2) = 70

Reorder the terms:
5(-2 + a)(-2 + a) = 70

Multiply (-2 + a) * (-2 + a)
5(-2(-2 + a) + a(-2 + a)) = 70
5((-2 * -2 + a * -2) + a(-2 + a)) = 70
5((4 + -2a) + a(-2 + a)) = 70
5(4 + -2a + (-2 * a + a * a)) = 70
5(4 + -2a + (-2a + a2)) = 70

Combine like terms: -2a + -2a = -4a
5(4 + -4a + a2) = 70
(4 * 5 + -4a * 5 + a2 * 5) = 70
(20 + -20a + 5a2) = 70

Solving
20 + -20a + 5a2 = 70

Solving for variable 'a'.

Reorder the terms:
20 + -70 + -20a + 5a2 = 70 + -70

Combine like terms: 20 + -70 = -50
-50 + -20a + 5a2 = 70 + -70

Combine like terms: 70 + -70 = 0
-50 + -20a + 5a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-10 + -4a + a2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-10 + -4a + a2)' equal to zero and attempt to solve:

Simplifying
-10 + -4a + a2 = 0

Solving
-10 + -4a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -4a + 10 + a2 = 0 + 10

Reorder the terms:
-10 + 10 + -4a + a2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -4a + a2 = 0 + 10
-4a + a2 = 0 + 10

Combine like terms: 0 + 10 = 10
-4a + a2 = 10

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 = 10 + 4

Reorder the terms:
4 + -4a + a2 = 10 + 4

Combine like terms: 10 + 4 = 14
4 + -4a + a2 = 14

Factor a perfect square on the left side:
(a + -2)(a + -2) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(a + -2) equal to 3.741657387 and -3.741657387.


Subproblem 1
a + -2 = 3.741657387

Simplifying
a + -2 = 3.741657387

Reorder the terms:
-2 + a = 3.741657387

Solving
-2 + a = 3.741657387

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 = 3.741657387 + 2

Combine like terms: -2 + 2 = 0
0 + a = 3.741657387 + 2
a = 3.741657387 + 2

Combine like terms: 3.741657387 + 2 = 5.741657387
a = 5.741657387

Simplifying
a = 5.741657387


Subproblem 2
a + -2 = -3.741657387

Simplifying
a + -2 = -3.741657387

Reorder the terms:
-2 + a = -3.741657387

Solving
-2 + a = -3.741657387

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 = -3.741657387 + 2

Combine like terms: -2 + 2 = 0
0 + a = -3.741657387 + 2
a = -3.741657387 + 2

Combine like terms: -3.741657387 + 2 = -1.741657387
a = -1.741657387

Simplifying
a = -1.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {5.741657387, -1.741657387}
Solution
a = {5.741657387, -1.741657387}

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