a^2-8a+14=0

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Solution for a^2-8a+14=0 equation:


Simplifying
a2 + -8a + 14 = 0

Reorder the terms:
14 + -8a + a2 = 0

Solving
14 + -8a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -8a + -14 + a2 = 0 + -14

Reorder the terms:
14 + -14 + -8a + a2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -8a + a2 = 0 + -14
-8a + a2 = 0 + -14

Combine like terms: 0 + -14 = -14
-8a + a2 = -14

The a term is -8a.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8a + 16 + a2 = -14 + 16

Reorder the terms:
16 + -8a + a2 = -14 + 16

Combine like terms: -14 + 16 = 2
16 + -8a + a2 = 2

Factor a perfect square on the left side:
(a + -4)(a + -4) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(a + -4) equal to 1.414213562 and -1.414213562.

Subproblem 1

a + -4 = 1.414213562 Simplifying a + -4 = 1.414213562 Reorder the terms: -4 + a = 1.414213562 Solving -4 + a = 1.414213562 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = 1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + a = 1.414213562 + 4 a = 1.414213562 + 4 Combine like terms: 1.414213562 + 4 = 5.414213562 a = 5.414213562 Simplifying a = 5.414213562

Subproblem 2

a + -4 = -1.414213562 Simplifying a + -4 = -1.414213562 Reorder the terms: -4 + a = -1.414213562 Solving -4 + a = -1.414213562 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = -1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + a = -1.414213562 + 4 a = -1.414213562 + 4 Combine like terms: -1.414213562 + 4 = 2.585786438 a = 2.585786438 Simplifying a = 2.585786438

Solution

The solution to the problem is based on the solutions from the subproblems. a = {5.414213562, 2.585786438}

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