# Solve for a a^2+(2b+6)^2=(2c+4)^2 a2+(2b+6)2=(2c+4)2
Simplify (2c+4)2.
Rewrite (2c+4)2 as (2c+4)(2c+4).
a2+(2b+6)2=(2c+4)(2c+4)
Expand (2c+4)(2c+4) using the FOIL Method.
Apply the distributive property.
a2+(2b+6)2=2c(2c+4)+4(2c+4)
Apply the distributive property.
a2+(2b+6)2=2c(2c)+2c⋅4+4(2c+4)
Apply the distributive property.
a2+(2b+6)2=2c(2c)+2c⋅4+4(2c)+4⋅4
a2+(2b+6)2=2c(2c)+2c⋅4+4(2c)+4⋅4
Simplify and combine like terms.
Simplify each term.
Multiply c by c.
a2+(2b+6)2=2⋅2c2+2c⋅4+4(2c)+4⋅4
Multiply 2 by 2.
a2+(2b+6)2=4c2+2c⋅4+4(2c)+4⋅4
Multiply 4 by 2.
a2+(2b+6)2=4c2+8c+4(2c)+4⋅4
Multiply 2 by 4.
a2+(2b+6)2=4c2+8c+8c+4⋅4
Multiply 4 by 4.
a2+(2b+6)2=4c2+8c+8c+16
a2+(2b+6)2=4c2+8c+8c+16
Add 8c and 8c.
a2+(2b+6)2=4c2+16c+16
a2+(2b+6)2=4c2+16c+16
a2+(2b+6)2=4c2+16c+16
Subtract (2b+6)2 from both sides of the equation.
a2=4c2+16c+16-(2b+6)2
Take the square root of both sides of the equation to eliminate the exponent on the left side.
a=±4c2+16c+16-(2b+6)2
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Factor using the perfect square rule.
Rewrite 4c2 as (2c)2.
a=±(2c)2+16c+16-(2b+6)2
Rewrite 16 as 42.
a=±(2c)2+16c+42-(2b+6)2
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅(2c)⋅4
Simplify.
2ab=16c
Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2, where a=2c and b=4.
a=±(2c+4)2-(2b+6)2
a=±(2c+4)2-(2b+6)2
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=2c+4 and b=2b+6.
a=±(2c+4+2b+6)(2c+4-(2b+6))
Simplify.
Add 4 and 6.
a=±(2c+2b+10)(2c+4-(2b+6))
Factor 2 out of 2c+2b+10.
Factor 2 out of 2c.
a=±(2(c)+2b+10)(2c+4-(2b+6))
Factor 2 out of 2b.
a=±(2(c)+2(b)+10)(2c+4-(2b+6))
Factor 2 out of 10.
a=±(2(c)+2b+2⋅5)(2c+4-(2b+6))
Factor 2 out of 2(c)+2b.
a=±(2(c+b)+2⋅5)(2c+4-(2b+6))
Factor 2 out of 2(c+b)+2⋅5.
a=±2(c+b+5)(2c+4-(2b+6))
a=±2(c+b+5)(2c+4-(2b+6))
Apply the distributive property.
a=±2(c+b+5)(2c+4-(2b)-1⋅6)
Multiply 2 by -1.
a=±2(c+b+5)(2c+4-2b-1⋅6)
Multiply -1 by 6.
a=±2(c+b+5)(2c+4-2b-6)
Subtract 6 from 4.
a=±2(c+b+5)(2c-2b-2)
Factor 2 out of 2c-2b-2.
Factor 2 out of 2c.
a=±2(c+b+5)(2(c)-2b-2)
Factor 2 out of -2b.
a=±2(c+b+5)(2(c)+2(-b)-2)
Factor 2 out of -2.
a=±2(c+b+5)(2(c)+2(-b)+2(-1))
Factor 2 out of 2(c)+2(-b).
a=±2(c+b+5)(2(c-b)+2(-1))
Factor 2 out of 2(c-b)+2(-1).
a=±2(c+b+5)(2(c-b-1))
a=±2(c+b+5)⋅(2(c-b-1))
Multiply 2 by 2.
a=±4(c+b+5)(c-b-1)
a=±4(c+b+5)(c-b-1)
Rewrite 4(c+b+5)(c-b-1) as 22((c+b+5)(c-b-1)).
Rewrite 4 as 22.
a=±22(c+b+5)(c-b-1)
a=±22((c+b+5)(c-b-1))
a=±22((c+b+5)(c-b-1))
Pull terms out from under the radical.
a=±2(c+b+5)(c-b-1)
a=±2(c+b+5)(c-b-1)
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
a=2(c+b+5)(c-b-1)
Next, use the negative value of the ± to find the second solution.
a=-2(c+b+5)(c-b-1)
The complete solution is the result of both the positive and negative portions of the solution.
a=2(c+b+5)(c-b-1)
a=-2(c+b+5)(c-b-1)
a=2(c+b+5)(c-b-1)
a=-2(c+b+5)(c-b-1)
a=2(c+b+5)(c-b-1)
a=-2(c+b+5)(c-b-1)
Solve for a a^2+(2b+6)^2=(2c+4)^2

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