8z^2+29z-48=0

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Solution for 8z^2+29z-48=0 equation:


Simplifying
8z2 + 29z + -48 = 0

Reorder the terms:
-48 + 29z + 8z2 = 0

Solving
-48 + 29z + 8z2 = 0

Solving for variable 'z'.

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

Divide each side by '8'.
-6 + 3.625z + z2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3.625z + 6 + z2 = 0 + 6

Reorder the terms:
-6 + 6 + 3.625z + z2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 3.625z + z2 = 0 + 6
3.625z + z2 = 0 + 6

Combine like terms: 0 + 6 = 6
3.625z + z2 = 6

The z term is 3.625z.  Take half its coefficient (1.8125).
Square it (3.28515625) and add it to both sides.

Add '3.28515625' to each side of the equation.
3.625z + 3.28515625 + z2 = 6 + 3.28515625

Reorder the terms:
3.28515625 + 3.625z + z2 = 6 + 3.28515625

Combine like terms: 6 + 3.28515625 = 9.28515625
3.28515625 + 3.625z + z2 = 9.28515625

Factor a perfect square on the left side:
(z + 1.8125)(z + 1.8125) = 9.28515625

Calculate the square root of the right side: 3.047155436

Break this problem into two subproblems by setting 
(z + 1.8125) equal to 3.047155436 and -3.047155436.

Subproblem 1

z + 1.8125 = 3.047155436 Simplifying z + 1.8125 = 3.047155436 Reorder the terms: 1.8125 + z = 3.047155436 Solving 1.8125 + z = 3.047155436 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.8125' to each side of the equation. 1.8125 + -1.8125 + z = 3.047155436 + -1.8125 Combine like terms: 1.8125 + -1.8125 = 0.0000 0.0000 + z = 3.047155436 + -1.8125 z = 3.047155436 + -1.8125 Combine like terms: 3.047155436 + -1.8125 = 1.234655436 z = 1.234655436 Simplifying z = 1.234655436

Subproblem 2

z + 1.8125 = -3.047155436 Simplifying z + 1.8125 = -3.047155436 Reorder the terms: 1.8125 + z = -3.047155436 Solving 1.8125 + z = -3.047155436 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.8125' to each side of the equation. 1.8125 + -1.8125 + z = -3.047155436 + -1.8125 Combine like terms: 1.8125 + -1.8125 = 0.0000 0.0000 + z = -3.047155436 + -1.8125 z = -3.047155436 + -1.8125 Combine like terms: -3.047155436 + -1.8125 = -4.859655436 z = -4.859655436 Simplifying z = -4.859655436

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.234655436, -4.859655436}

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