z^2+8z=15

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Solution for z^2+8z=15 equation:


Simplifying
z2 + 8z = 15

Reorder the terms:
8z + z2 = 15

Solving
8z + z2 = 15

Solving for variable 'z'.

Reorder the terms:
-15 + 8z + z2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 8z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 8z + 15 + z2 = 0 + 15

Reorder the terms:
-15 + 15 + 8z + z2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 8z + z2 = 0 + 15
8z + z2 = 0 + 15

Combine like terms: 0 + 15 = 15
8z + z2 = 15

The z term is 8z.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8z + 16 + z2 = 15 + 16

Reorder the terms:
16 + 8z + z2 = 15 + 16

Combine like terms: 15 + 16 = 31
16 + 8z + z2 = 31

Factor a perfect square on the left side:
(z + 4)(z + 4) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(z + 4) equal to 5.567764363 and -5.567764363.

Subproblem 1

z + 4 = 5.567764363 Simplifying z + 4 = 5.567764363 Reorder the terms: 4 + z = 5.567764363 Solving 4 + z = 5.567764363 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = 5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + z = 5.567764363 + -4 z = 5.567764363 + -4 Combine like terms: 5.567764363 + -4 = 1.567764363 z = 1.567764363 Simplifying z = 1.567764363

Subproblem 2

z + 4 = -5.567764363 Simplifying z + 4 = -5.567764363 Reorder the terms: 4 + z = -5.567764363 Solving 4 + z = -5.567764363 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = -5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + z = -5.567764363 + -4 z = -5.567764363 + -4 Combine like terms: -5.567764363 + -4 = -9.567764363 z = -9.567764363 Simplifying z = -9.567764363

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.567764363, -9.567764363}

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