s^2-8s-3=0

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Solution for s^2-8s-3=0 equation:


Simplifying
s2 + -8s + -3 = 0

Reorder the terms:
-3 + -8s + s2 = 0

Solving
-3 + -8s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -8s + 3 + s2 = 0 + 3

Reorder the terms:
-3 + 3 + -8s + s2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8s + s2 = 0 + 3
-8s + s2 = 0 + 3

Combine like terms: 0 + 3 = 3
-8s + s2 = 3

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

Add '16' to each side of the equation.
-8s + 16 + s2 = 3 + 16

Reorder the terms:
16 + -8s + s2 = 3 + 16

Combine like terms: 3 + 16 = 19
16 + -8s + s2 = 19

Factor a perfect square on the left side:
(s + -4)(s + -4) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(s + -4) equal to 4.358898944 and -4.358898944.

Subproblem 1

s + -4 = 4.358898944 Simplifying s + -4 = 4.358898944 Reorder the terms: -4 + s = 4.358898944 Solving -4 + s = 4.358898944 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + s = 4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + s = 4.358898944 + 4 s = 4.358898944 + 4 Combine like terms: 4.358898944 + 4 = 8.358898944 s = 8.358898944 Simplifying s = 8.358898944

Subproblem 2

s + -4 = -4.358898944 Simplifying s + -4 = -4.358898944 Reorder the terms: -4 + s = -4.358898944 Solving -4 + s = -4.358898944 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + s = -4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + s = -4.358898944 + 4 s = -4.358898944 + 4 Combine like terms: -4.358898944 + 4 = -0.358898944 s = -0.358898944 Simplifying s = -0.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. s = {8.358898944, -0.358898944}

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