a^2+21a-10=0

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Solution for a^2+21a-10=0 equation:


Simplifying
a2 + 21a + -10 = 0

Reorder the terms:
-10 + 21a + a2 = 0

Solving
-10 + 21a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 21a + 10 + a2 = 0 + 10

Reorder the terms:
-10 + 10 + 21a + a2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 21a + a2 = 0 + 10
21a + a2 = 0 + 10

Combine like terms: 0 + 10 = 10
21a + a2 = 10

The a term is 21a.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21a + 110.25 + a2 = 10 + 110.25

Reorder the terms:
110.25 + 21a + a2 = 10 + 110.25

Combine like terms: 10 + 110.25 = 120.25
110.25 + 21a + a2 = 120.25

Factor a perfect square on the left side:
(a + 10.5)(a + 10.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(a + 10.5) equal to 10.9658561 and -10.9658561.

Subproblem 1

a + 10.5 = 10.9658561 Simplifying a + 10.5 = 10.9658561 Reorder the terms: 10.5 + a = 10.9658561 Solving 10.5 + a = 10.9658561 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + a = 10.9658561 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + a = 10.9658561 + -10.5 a = 10.9658561 + -10.5 Combine like terms: 10.9658561 + -10.5 = 0.4658561 a = 0.4658561 Simplifying a = 0.4658561

Subproblem 2

a + 10.5 = -10.9658561 Simplifying a + 10.5 = -10.9658561 Reorder the terms: 10.5 + a = -10.9658561 Solving 10.5 + a = -10.9658561 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + a = -10.9658561 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + a = -10.9658561 + -10.5 a = -10.9658561 + -10.5 Combine like terms: -10.9658561 + -10.5 = -21.4658561 a = -21.4658561 Simplifying a = -21.4658561

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.4658561, -21.4658561}

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