z^2-30z=-37

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Solution for z^2-30z=-37 equation:


Simplifying
z2 + -30z = -37

Reorder the terms:
-30z + z2 = -37

Solving
-30z + z2 = -37

Solving for variable 'z'.

Reorder the terms:
37 + -30z + z2 = -37 + 37

Combine like terms: -37 + 37 = 0
37 + -30z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-37' to each side of the equation.
37 + -30z + -37 + z2 = 0 + -37

Reorder the terms:
37 + -37 + -30z + z2 = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -30z + z2 = 0 + -37
-30z + z2 = 0 + -37

Combine like terms: 0 + -37 = -37
-30z + z2 = -37

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 = -37 + 225

Reorder the terms:
225 + -30z + z2 = -37 + 225

Combine like terms: -37 + 225 = 188
225 + -30z + z2 = 188

Factor a perfect square on the left side:
(z + -15)(z + -15) = 188

Calculate the square root of the right side: 13.711309201

Break this problem into two subproblems by setting 
(z + -15) equal to 13.711309201 and -13.711309201.

Subproblem 1

z + -15 = 13.711309201 Simplifying z + -15 = 13.711309201 Reorder the terms: -15 + z = 13.711309201 Solving -15 + z = 13.711309201 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 = 13.711309201 + 15 Combine like terms: -15 + 15 = 0 0 + z = 13.711309201 + 15 z = 13.711309201 + 15 Combine like terms: 13.711309201 + 15 = 28.711309201 z = 28.711309201 Simplifying z = 28.711309201

Subproblem 2

z + -15 = -13.711309201 Simplifying z + -15 = -13.711309201 Reorder the terms: -15 + z = -13.711309201 Solving -15 + z = -13.711309201 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 = -13.711309201 + 15 Combine like terms: -15 + 15 = 0 0 + z = -13.711309201 + 15 z = -13.711309201 + 15 Combine like terms: -13.711309201 + 15 = 1.288690799 z = 1.288690799 Simplifying z = 1.288690799

Solution

The solution to the problem is based on the solutions from the subproblems. z = {28.711309201, 1.288690799}

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