b^2+3b-35=0

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Solution for b^2+3b-35=0 equation:


Simplifying
b2 + 3b + -35 = 0

Reorder the terms:
-35 + 3b + b2 = 0

Solving
-35 + 3b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 3b + 35 + b2 = 0 + 35

Reorder the terms:
-35 + 35 + 3b + b2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 3b + b2 = 0 + 35
3b + b2 = 0 + 35

Combine like terms: 0 + 35 = 35
3b + b2 = 35

The b term is 3b.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3b + 2.25 + b2 = 35 + 2.25

Reorder the terms:
2.25 + 3b + b2 = 35 + 2.25

Combine like terms: 35 + 2.25 = 37.25
2.25 + 3b + b2 = 37.25

Factor a perfect square on the left side:
(b + 1.5)(b + 1.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(b + 1.5) equal to 6.103277808 and -6.103277808.

Subproblem 1

b + 1.5 = 6.103277808 Simplifying b + 1.5 = 6.103277808 Reorder the terms: 1.5 + b = 6.103277808 Solving 1.5 + b = 6.103277808 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + b = 6.103277808 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = 6.103277808 + -1.5 b = 6.103277808 + -1.5 Combine like terms: 6.103277808 + -1.5 = 4.603277808 b = 4.603277808 Simplifying b = 4.603277808

Subproblem 2

b + 1.5 = -6.103277808 Simplifying b + 1.5 = -6.103277808 Reorder the terms: 1.5 + b = -6.103277808 Solving 1.5 + b = -6.103277808 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + b = -6.103277808 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = -6.103277808 + -1.5 b = -6.103277808 + -1.5 Combine like terms: -6.103277808 + -1.5 = -7.603277808 b = -7.603277808 Simplifying b = -7.603277808

Solution

The solution to the problem is based on the solutions from the subproblems. b = {4.603277808, -7.603277808}

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