(2s-3)(s+3)=228

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Solution for (2s-3)(s+3)=228 equation:


Simplifying
(2s + -3)(s + 3) = 228

Reorder the terms:
(-3 + 2s)(s + 3) = 228

Reorder the terms:
(-3 + 2s)(3 + s) = 228

Multiply (-3 + 2s) * (3 + s)
(-3(3 + s) + 2s * (3 + s)) = 228
((3 * -3 + s * -3) + 2s * (3 + s)) = 228
((-9 + -3s) + 2s * (3 + s)) = 228
(-9 + -3s + (3 * 2s + s * 2s)) = 228
(-9 + -3s + (6s + 2s2)) = 228

Combine like terms: -3s + 6s = 3s
(-9 + 3s + 2s2) = 228

Solving
-9 + 3s + 2s2 = 228

Solving for variable 's'.

Reorder the terms:
-9 + -228 + 3s + 2s2 = 228 + -228

Combine like terms: -9 + -228 = -237
-237 + 3s + 2s2 = 228 + -228

Combine like terms: 228 + -228 = 0
-237 + 3s + 2s2 = 0

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

Divide each side by '2'.
-118.5 + 1.5s + s2 = 0

Move the constant term to the right:

Add '118.5' to each side of the equation.
-118.5 + 1.5s + 118.5 + s2 = 0 + 118.5

Reorder the terms:
-118.5 + 118.5 + 1.5s + s2 = 0 + 118.5

Combine like terms: -118.5 + 118.5 = 0.0
0.0 + 1.5s + s2 = 0 + 118.5
1.5s + s2 = 0 + 118.5

Combine like terms: 0 + 118.5 = 118.5
1.5s + s2 = 118.5

The s term is 1.5s.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5s + 0.5625 + s2 = 118.5 + 0.5625

Reorder the terms:
0.5625 + 1.5s + s2 = 118.5 + 0.5625

Combine like terms: 118.5 + 0.5625 = 119.0625
0.5625 + 1.5s + s2 = 119.0625

Factor a perfect square on the left side:
(s + 0.75)(s + 0.75) = 119.0625

Calculate the square root of the right side: 10.911576421

Break this problem into two subproblems by setting 
(s + 0.75) equal to 10.911576421 and -10.911576421.

Subproblem 1

s + 0.75 = 10.911576421 Simplifying s + 0.75 = 10.911576421 Reorder the terms: 0.75 + s = 10.911576421 Solving 0.75 + s = 10.911576421 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + s = 10.911576421 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + s = 10.911576421 + -0.75 s = 10.911576421 + -0.75 Combine like terms: 10.911576421 + -0.75 = 10.161576421 s = 10.161576421 Simplifying s = 10.161576421

Subproblem 2

s + 0.75 = -10.911576421 Simplifying s + 0.75 = -10.911576421 Reorder the terms: 0.75 + s = -10.911576421 Solving 0.75 + s = -10.911576421 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + s = -10.911576421 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + s = -10.911576421 + -0.75 s = -10.911576421 + -0.75 Combine like terms: -10.911576421 + -0.75 = -11.661576421 s = -11.661576421 Simplifying s = -11.661576421

Solution

The solution to the problem is based on the solutions from the subproblems. s = {10.161576421, -11.661576421}

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