a^2-10a-20=5

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Solution for a^2-10a-20=5 equation:


Simplifying
a2 + -10a + -20 = 5

Reorder the terms:
-20 + -10a + a2 = 5

Solving
-20 + -10a + a2 = 5

Solving for variable 'a'.

Reorder the terms:
-20 + -5 + -10a + a2 = 5 + -5

Combine like terms: -20 + -5 = -25
-25 + -10a + a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-25 + -10a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -10a + 25 + a2 = 0 + 25

Reorder the terms:
-25 + 25 + -10a + a2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -10a + a2 = 0 + 25
-10a + a2 = 0 + 25

Combine like terms: 0 + 25 = 25
-10a + a2 = 25

The a term is -10a.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10a + 25 + a2 = 25 + 25

Reorder the terms:
25 + -10a + a2 = 25 + 25

Combine like terms: 25 + 25 = 50
25 + -10a + a2 = 50

Factor a perfect square on the left side:
(a + -5)(a + -5) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(a + -5) equal to 7.071067812 and -7.071067812.

Subproblem 1

a + -5 = 7.071067812 Simplifying a + -5 = 7.071067812 Reorder the terms: -5 + a = 7.071067812 Solving -5 + a = 7.071067812 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + a = 7.071067812 + 5 a = 7.071067812 + 5 Combine like terms: 7.071067812 + 5 = 12.071067812 a = 12.071067812 Simplifying a = 12.071067812

Subproblem 2

a + -5 = -7.071067812 Simplifying a + -5 = -7.071067812 Reorder the terms: -5 + a = -7.071067812 Solving -5 + a = -7.071067812 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = -7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + a = -7.071067812 + 5 a = -7.071067812 + 5 Combine like terms: -7.071067812 + 5 = -2.071067812 a = -2.071067812 Simplifying a = -2.071067812

Solution

The solution to the problem is based on the solutions from the subproblems. a = {12.071067812, -2.071067812}

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