a^2-10a+13=7

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Solution for a^2-10a+13=7 equation:


Simplifying
a2 + -10a + 13 = 7

Reorder the terms:
13 + -10a + a2 = 7

Solving
13 + -10a + a2 = 7

Solving for variable 'a'.

Reorder the terms:
13 + -7 + -10a + a2 = 7 + -7

Combine like terms: 13 + -7 = 6
6 + -10a + a2 = 7 + -7

Combine like terms: 7 + -7 = 0
6 + -10a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -10a + -6 + a2 = 0 + -6

Reorder the terms:
6 + -6 + -10a + a2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -10a + a2 = 0 + -6
-10a + a2 = 0 + -6

Combine like terms: 0 + -6 = -6
-10a + a2 = -6

The a term is -10a.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10a + 25 + a2 = -6 + 25

Reorder the terms:
25 + -10a + a2 = -6 + 25

Combine like terms: -6 + 25 = 19
25 + -10a + a2 = 19

Factor a perfect square on the left side:
(a + -5)(a + -5) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(a + -5) equal to 4.358898944 and -4.358898944.

Subproblem 1

a + -5 = 4.358898944 Simplifying a + -5 = 4.358898944 Reorder the terms: -5 + a = 4.358898944 Solving -5 + a = 4.358898944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 4.358898944 + 5 Combine like terms: -5 + 5 = 0 0 + a = 4.358898944 + 5 a = 4.358898944 + 5 Combine like terms: 4.358898944 + 5 = 9.358898944 a = 9.358898944 Simplifying a = 9.358898944

Subproblem 2

a + -5 = -4.358898944 Simplifying a + -5 = -4.358898944 Reorder the terms: -5 + a = -4.358898944 Solving -5 + a = -4.358898944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = -4.358898944 + 5 Combine like terms: -5 + 5 = 0 0 + a = -4.358898944 + 5 a = -4.358898944 + 5 Combine like terms: -4.358898944 + 5 = 0.641101056 a = 0.641101056 Simplifying a = 0.641101056

Solution

The solution to the problem is based on the solutions from the subproblems. a = {9.358898944, 0.641101056}

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