a^2-21a+28=0

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Solution for a^2-21a+28=0 equation:


Simplifying
a2 + -21a + 28 = 0

Reorder the terms:
28 + -21a + a2 = 0

Solving
28 + -21a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -21a + -28 + a2 = 0 + -28

Reorder the terms:
28 + -28 + -21a + a2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -21a + a2 = 0 + -28
-21a + a2 = 0 + -28

Combine like terms: 0 + -28 = -28
-21a + a2 = -28

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 = -28 + 110.25

Reorder the terms:
110.25 + -21a + a2 = -28 + 110.25

Combine like terms: -28 + 110.25 = 82.25
110.25 + -21a + a2 = 82.25

Factor a perfect square on the left side:
(a + -10.5)(a + -10.5) = 82.25

Calculate the square root of the right side: 9.069178574

Break this problem into two subproblems by setting 
(a + -10.5) equal to 9.069178574 and -9.069178574.

Subproblem 1

a + -10.5 = 9.069178574 Simplifying a + -10.5 = 9.069178574 Reorder the terms: -10.5 + a = 9.069178574 Solving -10.5 + a = 9.069178574 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 = 9.069178574 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = 9.069178574 + 10.5 a = 9.069178574 + 10.5 Combine like terms: 9.069178574 + 10.5 = 19.569178574 a = 19.569178574 Simplifying a = 19.569178574

Subproblem 2

a + -10.5 = -9.069178574 Simplifying a + -10.5 = -9.069178574 Reorder the terms: -10.5 + a = -9.069178574 Solving -10.5 + a = -9.069178574 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 = -9.069178574 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + a = -9.069178574 + 10.5 a = -9.069178574 + 10.5 Combine like terms: -9.069178574 + 10.5 = 1.430821426 a = 1.430821426 Simplifying a = 1.430821426

Solution

The solution to the problem is based on the solutions from the subproblems. a = {19.569178574, 1.430821426}

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