s^2-6s-10=0

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Solution for s^2-6s-10=0 equation:


Simplifying
s2 + -6s + -10 = 0

Reorder the terms:
-10 + -6s + s2 = 0

Solving
-10 + -6s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -6s + 10 + s2 = 0 + 10

Reorder the terms:
-10 + 10 + -6s + s2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -6s + s2 = 0 + 10
-6s + s2 = 0 + 10

Combine like terms: 0 + 10 = 10
-6s + s2 = 10

The s term is -6s.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6s + 9 + s2 = 10 + 9

Reorder the terms:
9 + -6s + s2 = 10 + 9

Combine like terms: 10 + 9 = 19
9 + -6s + s2 = 19

Factor a perfect square on the left side:
(s + -3)(s + -3) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(s + -3) equal to 4.358898944 and -4.358898944.

Subproblem 1

s + -3 = 4.358898944 Simplifying s + -3 = 4.358898944 Reorder the terms: -3 + s = 4.358898944 Solving -3 + s = 4.358898944 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + s = 4.358898944 + 3 Combine like terms: -3 + 3 = 0 0 + s = 4.358898944 + 3 s = 4.358898944 + 3 Combine like terms: 4.358898944 + 3 = 7.358898944 s = 7.358898944 Simplifying s = 7.358898944

Subproblem 2

s + -3 = -4.358898944 Simplifying s + -3 = -4.358898944 Reorder the terms: -3 + s = -4.358898944 Solving -3 + s = -4.358898944 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + s = -4.358898944 + 3 Combine like terms: -3 + 3 = 0 0 + s = -4.358898944 + 3 s = -4.358898944 + 3 Combine like terms: -4.358898944 + 3 = -1.358898944 s = -1.358898944 Simplifying s = -1.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. s = {7.358898944, -1.358898944}

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