2z^2+4z+4=9

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Solution for 2z^2+4z+4=9 equation:


Simplifying
2z2 + 4z + 4 = 9

Reorder the terms:
4 + 4z + 2z2 = 9

Solving
4 + 4z + 2z2 = 9

Solving for variable 'z'.

Reorder the terms:
4 + -9 + 4z + 2z2 = 9 + -9

Combine like terms: 4 + -9 = -5
-5 + 4z + 2z2 = 9 + -9

Combine like terms: 9 + -9 = 0
-5 + 4z + 2z2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-2.5 + 2z + z2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 2z + 2.5 + z2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 2z + z2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 2z + z2 = 0 + 2.5
2z + z2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
2z + z2 = 2.5

The z term is 2z.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2z + 1 + z2 = 2.5 + 1

Reorder the terms:
1 + 2z + z2 = 2.5 + 1

Combine like terms: 2.5 + 1 = 3.5
1 + 2z + z2 = 3.5

Factor a perfect square on the left side:
(z + 1)(z + 1) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(z + 1) equal to 1.870828693 and -1.870828693.

Subproblem 1

z + 1 = 1.870828693 Simplifying z + 1 = 1.870828693 Reorder the terms: 1 + z = 1.870828693 Solving 1 + z = 1.870828693 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = 1.870828693 + -1 Combine like terms: 1 + -1 = 0 0 + z = 1.870828693 + -1 z = 1.870828693 + -1 Combine like terms: 1.870828693 + -1 = 0.870828693 z = 0.870828693 Simplifying z = 0.870828693

Subproblem 2

z + 1 = -1.870828693 Simplifying z + 1 = -1.870828693 Reorder the terms: 1 + z = -1.870828693 Solving 1 + z = -1.870828693 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = -1.870828693 + -1 Combine like terms: 1 + -1 = 0 0 + z = -1.870828693 + -1 z = -1.870828693 + -1 Combine like terms: -1.870828693 + -1 = -2.870828693 z = -2.870828693 Simplifying z = -2.870828693

Solution

The solution to the problem is based on the solutions from the subproblems. z = {0.870828693, -2.870828693}

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