z^2+z-15=0

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Solution for z^2+z-15=0 equation:


Simplifying
z2 + z + -15 = 0

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

Solving
-15 + z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
z + 0.25 + z2 = 15 + 0.25

Reorder the terms:
0.25 + z + z2 = 15 + 0.25

Combine like terms: 15 + 0.25 = 15.25
0.25 + z + z2 = 15.25

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(z + 0.5) equal to 3.905124838 and -3.905124838.

Subproblem 1

z + 0.5 = 3.905124838 Simplifying z + 0.5 = 3.905124838 Reorder the terms: 0.5 + z = 3.905124838 Solving 0.5 + z = 3.905124838 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = 3.905124838 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = 3.905124838 + -0.5 z = 3.905124838 + -0.5 Combine like terms: 3.905124838 + -0.5 = 3.405124838 z = 3.405124838 Simplifying z = 3.405124838

Subproblem 2

z + 0.5 = -3.905124838 Simplifying z + 0.5 = -3.905124838 Reorder the terms: 0.5 + z = -3.905124838 Solving 0.5 + z = -3.905124838 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = -3.905124838 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = -3.905124838 + -0.5 z = -3.905124838 + -0.5 Combine like terms: -3.905124838 + -0.5 = -4.405124838 z = -4.405124838 Simplifying z = -4.405124838

Solution

The solution to the problem is based on the solutions from the subproblems. z = {3.405124838, -4.405124838}

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