4s^2+28s+49=60

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Solution for 4s^2+28s+49=60 equation:


Simplifying
4s2 + 28s + 49 = 60

Reorder the terms:
49 + 28s + 4s2 = 60

Solving
49 + 28s + 4s2 = 60

Solving for variable 's'.

Reorder the terms:
49 + -60 + 28s + 4s2 = 60 + -60

Combine like terms: 49 + -60 = -11
-11 + 28s + 4s2 = 60 + -60

Combine like terms: 60 + -60 = 0
-11 + 28s + 4s2 = 0

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

Divide each side by '4'.
-2.75 + 7s + s2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + 7s + 2.75 + s2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + 7s + s2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + 7s + s2 = 0 + 2.75
7s + s2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
7s + s2 = 2.75

The s term is 7s.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7s + 12.25 + s2 = 2.75 + 12.25

Reorder the terms:
12.25 + 7s + s2 = 2.75 + 12.25

Combine like terms: 2.75 + 12.25 = 15
12.25 + 7s + s2 = 15

Factor a perfect square on the left side:
(s + 3.5)(s + 3.5) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(s + 3.5) equal to 3.872983346 and -3.872983346.

Subproblem 1

s + 3.5 = 3.872983346 Simplifying s + 3.5 = 3.872983346 Reorder the terms: 3.5 + s = 3.872983346 Solving 3.5 + s = 3.872983346 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + s = 3.872983346 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + s = 3.872983346 + -3.5 s = 3.872983346 + -3.5 Combine like terms: 3.872983346 + -3.5 = 0.372983346 s = 0.372983346 Simplifying s = 0.372983346

Subproblem 2

s + 3.5 = -3.872983346 Simplifying s + 3.5 = -3.872983346 Reorder the terms: 3.5 + s = -3.872983346 Solving 3.5 + s = -3.872983346 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + s = -3.872983346 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + s = -3.872983346 + -3.5 s = -3.872983346 + -3.5 Combine like terms: -3.872983346 + -3.5 = -7.372983346 s = -7.372983346 Simplifying s = -7.372983346

Solution

The solution to the problem is based on the solutions from the subproblems. s = {0.372983346, -7.372983346}

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