2b^2+5b-10=

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Solution for 2b^2+5b-10= equation:


Simplifying
2b2 + 5b + -10 = 0

Reorder the terms:
-10 + 5b + 2b2 = 0

Solving
-10 + 5b + 2b2 = 0

Solving for variable 'b'.

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

Divide each side by '2'.
-5 + 2.5b + b2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2.5b + 5 + b2 = 0 + 5

Reorder the terms:
-5 + 5 + 2.5b + b2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2.5b + b2 = 0 + 5
2.5b + b2 = 0 + 5

Combine like terms: 0 + 5 = 5
2.5b + b2 = 5

The b term is 2.5b.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5b + 1.5625 + b2 = 5 + 1.5625

Reorder the terms:
1.5625 + 2.5b + b2 = 5 + 1.5625

Combine like terms: 5 + 1.5625 = 6.5625
1.5625 + 2.5b + b2 = 6.5625

Factor a perfect square on the left side:
(b + 1.25)(b + 1.25) = 6.5625

Calculate the square root of the right side: 2.561737691

Break this problem into two subproblems by setting 
(b + 1.25) equal to 2.561737691 and -2.561737691.

Subproblem 1

b + 1.25 = 2.561737691 Simplifying b + 1.25 = 2.561737691 Reorder the terms: 1.25 + b = 2.561737691 Solving 1.25 + b = 2.561737691 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + b = 2.561737691 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + b = 2.561737691 + -1.25 b = 2.561737691 + -1.25 Combine like terms: 2.561737691 + -1.25 = 1.311737691 b = 1.311737691 Simplifying b = 1.311737691

Subproblem 2

b + 1.25 = -2.561737691 Simplifying b + 1.25 = -2.561737691 Reorder the terms: 1.25 + b = -2.561737691 Solving 1.25 + b = -2.561737691 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + b = -2.561737691 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + b = -2.561737691 + -1.25 b = -2.561737691 + -1.25 Combine like terms: -2.561737691 + -1.25 = -3.811737691 b = -3.811737691 Simplifying b = -3.811737691

Solution

The solution to the problem is based on the solutions from the subproblems. b = {1.311737691, -3.811737691}

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