z^2-15z+12=

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Solution for z^2-15z+12= equation:


Simplifying
z2 + -15z + 12 = 0

Reorder the terms:
12 + -15z + z2 = 0

Solving
12 + -15z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -15z + -12 + z2 = 0 + -12

Reorder the terms:
12 + -12 + -15z + z2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -15z + z2 = 0 + -12
-15z + z2 = 0 + -12

Combine like terms: 0 + -12 = -12
-15z + z2 = -12

The z term is -15z.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15z + 56.25 + z2 = -12 + 56.25

Reorder the terms:
56.25 + -15z + z2 = -12 + 56.25

Combine like terms: -12 + 56.25 = 44.25
56.25 + -15z + z2 = 44.25

Factor a perfect square on the left side:
(z + -7.5)(z + -7.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(z + -7.5) equal to 6.652067348 and -6.652067348.

Subproblem 1

z + -7.5 = 6.652067348 Simplifying z + -7.5 = 6.652067348 Reorder the terms: -7.5 + z = 6.652067348 Solving -7.5 + z = 6.652067348 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + z = 6.652067348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + z = 6.652067348 + 7.5 z = 6.652067348 + 7.5 Combine like terms: 6.652067348 + 7.5 = 14.152067348 z = 14.152067348 Simplifying z = 14.152067348

Subproblem 2

z + -7.5 = -6.652067348 Simplifying z + -7.5 = -6.652067348 Reorder the terms: -7.5 + z = -6.652067348 Solving -7.5 + z = -6.652067348 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + z = -6.652067348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + z = -6.652067348 + 7.5 z = -6.652067348 + 7.5 Combine like terms: -6.652067348 + 7.5 = 0.847932652 z = 0.847932652 Simplifying z = 0.847932652

Solution

The solution to the problem is based on the solutions from the subproblems. z = {14.152067348, 0.847932652}

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