(2b-7)2=32

Take the square root of each side of the equation to set up the solution for b

(2b-7)2⋅12=±32

Remove the perfect root factor 2b-7 under the radical to solve for b.

2b-7=±32

Rewrite 32 as 42⋅2.

Factor 16 out of 32.

2b-7=±16(2)

Rewrite 16 as 42.

2b-7=±42⋅2

2b-7=±42⋅2

Pull terms out from under the radical.

2b-7=±42

2b-7=±42

First, use the positive value of the ± to find the first solution.

2b-7=42

Add 7 to both sides of the equation.

2b=42+7

Divide each term by 2 and simplify.

Divide each term in 2b=42+7 by 2.

2b2=422+72

Cancel the common factor of 2.

Cancel the common factor.

2b2=422+72

Divide b by 1.

b=422+72

b=422+72

Cancel the common factor of 4 and 2.

Factor 2 out of 42.

b=2(22)2+72

Cancel the common factors.

Factor 2 out of 2.

b=2(22)2(1)+72

Cancel the common factor.

b=2(22)2⋅1+72

Rewrite the expression.

b=221+72

Divide 22 by 1.

b=22+72

b=22+72

b=22+72

b=22+72

Next, use the negative value of the ± to find the second solution.

2b-7=-42

Add 7 to both sides of the equation.

2b=-42+7

Divide each term by 2 and simplify.

Divide each term in 2b=-42+7 by 2.

2b2=-422+72

Cancel the common factor of 2.

Cancel the common factor.

2b2=-422+72

Divide b by 1.

b=-422+72

b=-422+72

Cancel the common factor of -4 and 2.

Factor 2 out of -42.

b=2(-22)2+72

Cancel the common factors.

Factor 2 out of 2.

b=2(-22)2(1)+72

Cancel the common factor.

b=2(-22)2⋅1+72

Rewrite the expression.

b=-221+72

Divide -22 by 1.

b=-22+72

b=-22+72

b=-22+72

b=-22+72

The complete solution is the result of both the positive and negative portions of the solution.

b=22+72,-22+72

b=22+72,-22+72

The result can be shown in multiple forms.

Exact Form:

b=22+72,-22+72

Decimal Form:

b=6.32842712…,0.67157287…

Solve for b (2b-7)^2=32