s^2+16s=-45

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Solution for s^2+16s=-45 equation:


Simplifying
s2 + 16s = -45

Reorder the terms:
16s + s2 = -45

Solving
16s + s2 = -45

Solving for variable 's'.

Reorder the terms:
45 + 16s + s2 = -45 + 45

Combine like terms: -45 + 45 = 0
45 + 16s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + 16s + -45 + s2 = 0 + -45

Reorder the terms:
45 + -45 + 16s + s2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + 16s + s2 = 0 + -45
16s + s2 = 0 + -45

Combine like terms: 0 + -45 = -45
16s + s2 = -45

The s term is 16s.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16s + 64 + s2 = -45 + 64

Reorder the terms:
64 + 16s + s2 = -45 + 64

Combine like terms: -45 + 64 = 19
64 + 16s + s2 = 19

Factor a perfect square on the left side:
(s + 8)(s + 8) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(s + 8) equal to 4.358898944 and -4.358898944.

Subproblem 1

s + 8 = 4.358898944 Simplifying s + 8 = 4.358898944 Reorder the terms: 8 + s = 4.358898944 Solving 8 + s = 4.358898944 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + s = 4.358898944 + -8 Combine like terms: 8 + -8 = 0 0 + s = 4.358898944 + -8 s = 4.358898944 + -8 Combine like terms: 4.358898944 + -8 = -3.641101056 s = -3.641101056 Simplifying s = -3.641101056

Subproblem 2

s + 8 = -4.358898944 Simplifying s + 8 = -4.358898944 Reorder the terms: 8 + s = -4.358898944 Solving 8 + s = -4.358898944 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + s = -4.358898944 + -8 Combine like terms: 8 + -8 = 0 0 + s = -4.358898944 + -8 s = -4.358898944 + -8 Combine like terms: -4.358898944 + -8 = -12.358898944 s = -12.358898944 Simplifying s = -12.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. s = {-3.641101056, -12.358898944}

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