z^2-30z=-43

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Solution for z^2-30z=-43 equation:


Simplifying
z2 + -30z = -43

Reorder the terms:
-30z + z2 = -43

Solving
-30z + z2 = -43

Solving for variable 'z'.

Reorder the terms:
43 + -30z + z2 = -43 + 43

Combine like terms: -43 + 43 = 0
43 + -30z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-43' to each side of the equation.
43 + -30z + -43 + z2 = 0 + -43

Reorder the terms:
43 + -43 + -30z + z2 = 0 + -43

Combine like terms: 43 + -43 = 0
0 + -30z + z2 = 0 + -43
-30z + z2 = 0 + -43

Combine like terms: 0 + -43 = -43
-30z + z2 = -43

The z term is -30z.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30z + 225 + z2 = -43 + 225

Reorder the terms:
225 + -30z + z2 = -43 + 225

Combine like terms: -43 + 225 = 182
225 + -30z + z2 = 182

Factor a perfect square on the left side:
(z + -15)(z + -15) = 182

Calculate the square root of the right side: 13.490737563

Break this problem into two subproblems by setting 
(z + -15) equal to 13.490737563 and -13.490737563.

Subproblem 1

z + -15 = 13.490737563 Simplifying z + -15 = 13.490737563 Reorder the terms: -15 + z = 13.490737563 Solving -15 + z = 13.490737563 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + z = 13.490737563 + 15 Combine like terms: -15 + 15 = 0 0 + z = 13.490737563 + 15 z = 13.490737563 + 15 Combine like terms: 13.490737563 + 15 = 28.490737563 z = 28.490737563 Simplifying z = 28.490737563

Subproblem 2

z + -15 = -13.490737563 Simplifying z + -15 = -13.490737563 Reorder the terms: -15 + z = -13.490737563 Solving -15 + z = -13.490737563 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + z = -13.490737563 + 15 Combine like terms: -15 + 15 = 0 0 + z = -13.490737563 + 15 z = -13.490737563 + 15 Combine like terms: -13.490737563 + 15 = 1.509262437 z = 1.509262437 Simplifying z = 1.509262437

Solution

The solution to the problem is based on the solutions from the subproblems. z = {28.490737563, 1.509262437}

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