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42 votes
42 votes
2b square (7b squared to the third- 10)

User Sauntimo
by
2.5k points

1 Answer

8 votes
8 votes

Simplifying

2b2 + -7b + -3 = 0

Reorder the terms:

-3 + -7b + 2b2 = 0

Solving

-3 + -7b + 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'.

-1.5 + -3.5b + b2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.

-1.5 + -3.5b + 1.5 + b2 = 0 + 1.5

Reorder the terms:

-1.5 + 1.5 + -3.5b + b2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0

0.0 + -3.5b + b2 = 0 + 1.5

-3.5b + b2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5

-3.5b + b2 = 1.5

The b term is -3.5b. Take half its coefficient (-1.75).

Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.

-3.5b + 3.0625 + b2 = 1.5 + 3.0625

Reorder the terms:

3.0625 + -3.5b + b2 = 1.5 + 3.0625

Combine like terms: 1.5 + 3.0625 = 4.5625

3.0625 + -3.5b + b2 = 4.5625

Factor a perfect square on the left side:

(b + -1.75)(b + -1.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting

(b + -1.75) equal to 2.136000936 and -2.136000936.

Subproblem 1

b + -1.75 = 2.136000936

Simplifying

b + -1.75 = 2.136000936

Reorder the terms:

-1.75 + b = 2.136000936

Solving

-1.75 + b = 2.136000936

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '1.75' to each side of the equation.

-1.75 + 1.75 + b = 2.136000936 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00

0.00 + b = 2.136000936 + 1.75

b = 2.136000936 + 1.75

Combine like terms: 2.136000936 + 1.75 = 3.886000936

b = 3.886000936

Simplifying

b = 3.886000936

Subproblem 2

b + -1.75 = -2.136000936

Simplifying

b + -1.75 = -2.136000936

Reorder the terms:

-1.75 + b = -2.136000936

Solving

-1.75 + b = -2.136000936

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '1.75' to each side of the equation.

-1.75 + 1.75 + b = -2.136000936 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00

0.00 + b = -2.136000936 + 1.75

b = -2.136000936 + 1.75

Combine like terms: -2.136000936 + 1.75 = -0.386000936

b = -0.386000936

Simplifying

b = -0.386000936

Solution

The solution to the problem is based on the solutions

from the subproblems.

b = {3.886000936, -0.386000936}

User Kathalina
by
3.1k points