Solve for a a^2+(2b+6)^2=(2c+4)^2

Math
a2+(2b+6)2=(2c+4)2
Simplify (2c+4)2.
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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.
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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.
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Simplify each term.
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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.
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Simplify the right side of the equation.
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Factor using the perfect square rule.
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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.
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Add 4 and 6.
a=±(2c+2b+10)(2c+4-(2b+6))
Factor 2 out of 2c+2b+10.
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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.
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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)).
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Rewrite 4 as 22.
a=±22(c+b+5)(c-b-1)
Add parentheses.
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.
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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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