a^2-21a+56=0

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Solution for a^2-21a+56=0 equation:


Simplifying
a2 + -21a + 56 = 0

Reorder the terms:
56 + -21a + a2 = 0

Solving
56 + -21a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-56' to each side of the equation.
56 + -21a + -56 + a2 = 0 + -56

Reorder the terms:
56 + -56 + -21a + a2 = 0 + -56

Combine like terms: 56 + -56 = 0
0 + -21a + a2 = 0 + -56
-21a + a2 = 0 + -56

Combine like terms: 0 + -56 = -56
-21a + a2 = -56

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 = -56 + 110.25

Reorder the terms:
110.25 + -21a + a2 = -56 + 110.25

Combine like terms: -56 + 110.25 = 54.25
110.25 + -21a + a2 = 54.25

Factor a perfect square on the left side:
(a + -10.5)(a + -10.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(a + -10.5) equal to 7.365459931 and -7.365459931.

Subproblem 1

a + -10.5 = 7.365459931 Simplifying a + -10.5 = 7.365459931 Reorder the terms: -10.5 + a = 7.365459931 Solving -10.5 + a = 7.365459931 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 = 7.365459931 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = 7.365459931 + 10.5 a = 7.365459931 + 10.5 Combine like terms: 7.365459931 + 10.5 = 17.865459931 a = 17.865459931 Simplifying a = 17.865459931

Subproblem 2

a + -10.5 = -7.365459931 Simplifying a + -10.5 = -7.365459931 Reorder the terms: -10.5 + a = -7.365459931 Solving -10.5 + a = -7.365459931 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 = -7.365459931 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = -7.365459931 + 10.5 a = -7.365459931 + 10.5 Combine like terms: -7.365459931 + 10.5 = 3.134540069 a = 3.134540069 Simplifying a = 3.134540069

Solution

The solution to the problem is based on the solutions from the subproblems. a = {17.865459931, 3.134540069}

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