z^2-20z=-15

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Solution for z^2-20z=-15 equation:


Simplifying
z2 + -20z = -15

Reorder the terms:
-20z + z2 = -15

Solving
-20z + z2 = -15

Solving for variable 'z'.

Reorder the terms:
15 + -20z + z2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + -20z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -20z + -15 + z2 = 0 + -15

Reorder the terms:
15 + -15 + -20z + z2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -20z + z2 = 0 + -15
-20z + z2 = 0 + -15

Combine like terms: 0 + -15 = -15
-20z + z2 = -15

The z term is -20z.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20z + 100 + z2 = -15 + 100

Reorder the terms:
100 + -20z + z2 = -15 + 100

Combine like terms: -15 + 100 = 85
100 + -20z + z2 = 85

Factor a perfect square on the left side:
(z + -10)(z + -10) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(z + -10) equal to 9.219544457 and -9.219544457.

Subproblem 1

z + -10 = 9.219544457 Simplifying z + -10 = 9.219544457 Reorder the terms: -10 + z = 9.219544457 Solving -10 + z = 9.219544457 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + z = 9.219544457 + 10 Combine like terms: -10 + 10 = 0 0 + z = 9.219544457 + 10 z = 9.219544457 + 10 Combine like terms: 9.219544457 + 10 = 19.219544457 z = 19.219544457 Simplifying z = 19.219544457

Subproblem 2

z + -10 = -9.219544457 Simplifying z + -10 = -9.219544457 Reorder the terms: -10 + z = -9.219544457 Solving -10 + z = -9.219544457 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + z = -9.219544457 + 10 Combine like terms: -10 + 10 = 0 0 + z = -9.219544457 + 10 z = -9.219544457 + 10 Combine like terms: -9.219544457 + 10 = 0.780455543 z = 0.780455543 Simplifying z = 0.780455543

Solution

The solution to the problem is based on the solutions from the subproblems. z = {19.219544457, 0.780455543}

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