3s^2+20s=180

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Solution for 3s^2+20s=180 equation:


Simplifying
3s2 + 20s = 180

Reorder the terms:
20s + 3s2 = 180

Solving
20s + 3s2 = 180

Solving for variable 's'.

Reorder the terms:
-180 + 20s + 3s2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 20s + 3s2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-60 + 6.666666667s + s2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 6.666666667s + 60 + s2 = 0 + 60

Reorder the terms:
-60 + 60 + 6.666666667s + s2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 6.666666667s + s2 = 0 + 60
6.666666667s + s2 = 0 + 60

Combine like terms: 0 + 60 = 60
6.666666667s + s2 = 60

The s term is 6.666666667s.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667s + 11.11111112 + s2 = 60 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667s + s2 = 60 + 11.11111112

Combine like terms: 60 + 11.11111112 = 71.11111112
11.11111112 + 6.666666667s + s2 = 71.11111112

Factor a perfect square on the left side:
(s + 3.333333334)(s + 3.333333334) = 71.11111112

Calculate the square root of the right side: 8.432740428

Break this problem into two subproblems by setting 
(s + 3.333333334) equal to 8.432740428 and -8.432740428.

Subproblem 1

s + 3.333333334 = 8.432740428 Simplifying s + 3.333333334 = 8.432740428 Reorder the terms: 3.333333334 + s = 8.432740428 Solving 3.333333334 + s = 8.432740428 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + s = 8.432740428 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + s = 8.432740428 + -3.333333334 s = 8.432740428 + -3.333333334 Combine like terms: 8.432740428 + -3.333333334 = 5.099407094 s = 5.099407094 Simplifying s = 5.099407094

Subproblem 2

s + 3.333333334 = -8.432740428 Simplifying s + 3.333333334 = -8.432740428 Reorder the terms: 3.333333334 + s = -8.432740428 Solving 3.333333334 + s = -8.432740428 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + s = -8.432740428 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + s = -8.432740428 + -3.333333334 s = -8.432740428 + -3.333333334 Combine like terms: -8.432740428 + -3.333333334 = -11.766073762 s = -11.766073762 Simplifying s = -11.766073762

Solution

The solution to the problem is based on the solutions from the subproblems. s = {5.099407094, -11.766073762}

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