2z^2-212z-36=0

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Solution for 2z^2-212z-36=0 equation:


Simplifying
2z2 + -212z + -36 = 0

Reorder the terms:
-36 + -212z + 2z2 = 0

Solving
-36 + -212z + 2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -106z + z2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-18 + -106z + z2)' equal to zero and attempt to solve: Simplifying -18 + -106z + z2 = 0 Solving -18 + -106z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -106z + 18 + z2 = 0 + 18 Reorder the terms: -18 + 18 + -106z + z2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -106z + z2 = 0 + 18 -106z + z2 = 0 + 18 Combine like terms: 0 + 18 = 18 -106z + z2 = 18 The z term is -106z. Take half its coefficient (-53). Square it (2809) and add it to both sides. Add '2809' to each side of the equation. -106z + 2809 + z2 = 18 + 2809 Reorder the terms: 2809 + -106z + z2 = 18 + 2809 Combine like terms: 18 + 2809 = 2827 2809 + -106z + z2 = 2827 Factor a perfect square on the left side: (z + -53)(z + -53) = 2827 Calculate the square root of the right side: 53.169540152 Break this problem into two subproblems by setting (z + -53) equal to 53.169540152 and -53.169540152.

Subproblem 1

z + -53 = 53.169540152 Simplifying z + -53 = 53.169540152 Reorder the terms: -53 + z = 53.169540152 Solving -53 + z = 53.169540152 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '53' to each side of the equation. -53 + 53 + z = 53.169540152 + 53 Combine like terms: -53 + 53 = 0 0 + z = 53.169540152 + 53 z = 53.169540152 + 53 Combine like terms: 53.169540152 + 53 = 106.169540152 z = 106.169540152 Simplifying z = 106.169540152

Subproblem 2

z + -53 = -53.169540152 Simplifying z + -53 = -53.169540152 Reorder the terms: -53 + z = -53.169540152 Solving -53 + z = -53.169540152 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '53' to each side of the equation. -53 + 53 + z = -53.169540152 + 53 Combine like terms: -53 + 53 = 0 0 + z = -53.169540152 + 53 z = -53.169540152 + 53 Combine like terms: -53.169540152 + 53 = -0.169540152 z = -0.169540152 Simplifying z = -0.169540152

Solution

The solution to the problem is based on the solutions from the subproblems. z = {106.169540152, -0.169540152}

Solution

z = {106.169540152, -0.169540152}

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