a^2-8a+10=0

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Solution for a^2-8a+10=0 equation:


Simplifying
a2 + -8a + 10 = 0

Reorder the terms:
10 + -8a + a2 = 0

Solving
10 + -8a + 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 + -8a + -10 + a2 = 0 + -10

Reorder the terms:
10 + -10 + -8a + a2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -8a + a2 = 0 + -10
-8a + a2 = 0 + -10

Combine like terms: 0 + -10 = -10
-8a + a2 = -10

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 = -10 + 16

Reorder the terms:
16 + -8a + a2 = -10 + 16

Combine like terms: -10 + 16 = 6
16 + -8a + a2 = 6

Factor a perfect square on the left side:
(a + -4)(a + -4) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(a + -4) equal to 2.449489743 and -2.449489743.

Subproblem 1

a + -4 = 2.449489743 Simplifying a + -4 = 2.449489743 Reorder the terms: -4 + a = 2.449489743 Solving -4 + a = 2.449489743 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 = 2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + a = 2.449489743 + 4 a = 2.449489743 + 4 Combine like terms: 2.449489743 + 4 = 6.449489743 a = 6.449489743 Simplifying a = 6.449489743

Subproblem 2

a + -4 = -2.449489743 Simplifying a + -4 = -2.449489743 Reorder the terms: -4 + a = -2.449489743 Solving -4 + a = -2.449489743 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 = -2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + a = -2.449489743 + 4 a = -2.449489743 + 4 Combine like terms: -2.449489743 + 4 = 1.550510257 a = 1.550510257 Simplifying a = 1.550510257

Solution

The solution to the problem is based on the solutions from the subproblems. a = {6.449489743, 1.550510257}

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