z^2-10z=-12

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Solution for z^2-10z=-12 equation:


Simplifying
z2 + -10z = -12

Reorder the terms:
-10z + z2 = -12

Solving
-10z + z2 = -12

Solving for variable 'z'.

Reorder the terms:
12 + -10z + z2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + -10z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -10z + -12 + z2 = 0 + -12

Reorder the terms:
12 + -12 + -10z + z2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -10z + z2 = 0 + -12
-10z + z2 = 0 + -12

Combine like terms: 0 + -12 = -12
-10z + z2 = -12

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

Add '25' to each side of the equation.
-10z + 25 + z2 = -12 + 25

Reorder the terms:
25 + -10z + z2 = -12 + 25

Combine like terms: -12 + 25 = 13
25 + -10z + z2 = 13

Factor a perfect square on the left side:
(z + -5)(z + -5) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(z + -5) equal to 3.605551275 and -3.605551275.

Subproblem 1

z + -5 = 3.605551275 Simplifying z + -5 = 3.605551275 Reorder the terms: -5 + z = 3.605551275 Solving -5 + z = 3.605551275 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = 3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + z = 3.605551275 + 5 z = 3.605551275 + 5 Combine like terms: 3.605551275 + 5 = 8.605551275 z = 8.605551275 Simplifying z = 8.605551275

Subproblem 2

z + -5 = -3.605551275 Simplifying z + -5 = -3.605551275 Reorder the terms: -5 + z = -3.605551275 Solving -5 + z = -3.605551275 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = -3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + z = -3.605551275 + 5 z = -3.605551275 + 5 Combine like terms: -3.605551275 + 5 = 1.394448725 z = 1.394448725 Simplifying z = 1.394448725

Solution

The solution to the problem is based on the solutions from the subproblems. z = {8.605551275, 1.394448725}

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