a^2-14a+28=

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Solution for a^2-14a+28= equation:


Simplifying
a2 + -14a + 28 = 0

Reorder the terms:
28 + -14a + a2 = 0

Solving
28 + -14a + 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 + -14a + -28 + a2 = 0 + -28

Reorder the terms:
28 + -28 + -14a + a2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -14a + a2 = 0 + -28
-14a + a2 = 0 + -28

Combine like terms: 0 + -28 = -28
-14a + a2 = -28

The a term is -14a.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14a + 49 + a2 = -28 + 49

Reorder the terms:
49 + -14a + a2 = -28 + 49

Combine like terms: -28 + 49 = 21
49 + -14a + a2 = 21

Factor a perfect square on the left side:
(a + -7)(a + -7) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(a + -7) equal to 4.582575695 and -4.582575695.

Subproblem 1

a + -7 = 4.582575695 Simplifying a + -7 = 4.582575695 Reorder the terms: -7 + a = 4.582575695 Solving -7 + a = 4.582575695 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = 4.582575695 + 7 Combine like terms: -7 + 7 = 0 0 + a = 4.582575695 + 7 a = 4.582575695 + 7 Combine like terms: 4.582575695 + 7 = 11.582575695 a = 11.582575695 Simplifying a = 11.582575695

Subproblem 2

a + -7 = -4.582575695 Simplifying a + -7 = -4.582575695 Reorder the terms: -7 + a = -4.582575695 Solving -7 + a = -4.582575695 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + a = -4.582575695 + 7 Combine like terms: -7 + 7 = 0 0 + a = -4.582575695 + 7 a = -4.582575695 + 7 Combine like terms: -4.582575695 + 7 = 2.417424305 a = 2.417424305 Simplifying a = 2.417424305

Solution

The solution to the problem is based on the solutions from the subproblems. a = {11.582575695, 2.417424305}

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