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

Math
(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
Simplify the right side of the equation.
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Rewrite 32 as 42⋅2.
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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
The complete solution is the result of both the positive and negative portions of the solution.
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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.
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Divide each term in 2b=42+7 by 2.
2b2=422+72
Cancel the common factor of 2.
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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.
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Factor 2 out of 42.
b=2(22)2+72
Cancel the common factors.
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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.
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Divide each term in 2b=-42+7 by 2.
2b2=-422+72
Cancel the common factor of 2.
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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.
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Factor 2 out of -42.
b=2(-22)2+72
Cancel the common factors.
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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

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