Solve Using the Square Root Property x^2+((4x+25)/3)^2=25

Math
x2+(4x+253)2=25
Factor the equation.
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Apply the product rule to 4x+253.
x2+(4x+25)232=25
Raise 3 to the power of 2.
x2+(4x+25)29=25
To write x2 as a fraction with a common denominator, multiply by 99.
x2⋅99+(4x+25)29=25
Combine x2 and 99.
x2⋅99+(4x+25)29=25
Combine the numerators over the common denominator.
x2⋅9+(4x+25)29=25
Rewrite x2⋅9+(4x+25)29 in a factored form.
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Move 9 to the left of x2.
9×2+(4x+25)29=25
Rewrite (4x+25)2 as (4x+25)(4x+25).
9×2+(4x+25)(4x+25)9=25
Expand (4x+25)(4x+25) using the FOIL Method.
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Apply the distributive property.
9×2+4x(4x+25)+25(4x+25)9=25
Apply the distributive property.
9×2+4x(4x)+4x⋅25+25(4x+25)9=25
Apply the distributive property.
9×2+4x(4x)+4x⋅25+25(4x)+25⋅259=25
9×2+4x(4x)+4x⋅25+25(4x)+25⋅259=25
Simplify and combine like terms.
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Simplify each term.
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Multiply x by x.
9×2+4⋅(4×2)+4x⋅25+25(4x)+25⋅259=25
Multiply 4 by 4.
9×2+16×2+4x⋅25+25(4x)+25⋅259=25
Multiply 25 by 4.
9×2+16×2+100x+25(4x)+25⋅259=25
Multiply 4 by 25.
9×2+16×2+100x+100x+25⋅259=25
Multiply 25 by 25.
9×2+16×2+100x+100x+6259=25
9×2+16×2+100x+100x+6259=25
Add 100x and 100x.
9×2+16×2+200x+6259=25
9×2+16×2+200x+6259=25
Add 9×2 and 16×2.
25×2+200x+6259=25
Factor 25 out of 25×2+200x+625.
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Factor 25 out of 25×2.
25(x2)+200x+6259=25
Factor 25 out of 200x.
25(x2)+25(8x)+6259=25
Factor 25 out of 625.
25×2+25(8x)+25⋅259=25
Factor 25 out of 25×2+25(8x).
25(x2+8x)+25⋅259=25
Factor 25 out of 25(x2+8x)+25⋅25.
25(x2+8x+25)9=25
25(x2+8x+25)9=25
25(x2+8x+25)9=25
25(x2+8x+25)9=25
Solve the equation.
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Multiply both sides of the equation by 9.
25(x2+8x+25)=25⋅(9)
Simplify 25(x2+8x+25).
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Apply the distributive property.
25×2+25(8x)+25⋅25=25⋅(9)
Simplify.
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Multiply 8 by 25.
25×2+200x+25⋅25=25⋅(9)
Multiply 25 by 25.
25×2+200x+625=25⋅(9)
25×2+200x+625=25⋅(9)
25×2+200x+625=25⋅(9)
Multiply 25 by 9.
25×2+200x+625=225
Move 225 to the left side of the equation by subtracting it from both sides.
25×2+200x+625-225=0
Subtract 225 from 625.
25×2+200x+400=0
Factor the left side of the equation.
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Factor 25 out of 25×2+200x+400.
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Factor 25 out of 25×2.
25(x2)+200x+400=0
Factor 25 out of 200x.
25(x2)+25(8x)+400=0
Factor 25 out of 400.
25×2+25(8x)+25⋅16=0
Factor 25 out of 25×2+25(8x).
25(x2+8x)+25⋅16=0
Factor 25 out of 25(x2+8x)+25⋅16.
25(x2+8x+16)=0
25(x2+8x+16)=0
Factor using the perfect square rule.
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Rewrite 16 as 42.
25(x2+8x+42)=0
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅x⋅4
Simplify.
2ab=8x
Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2, where a=x and b=4.
25(x+4)2=0
25(x+4)2=0
25(x+4)2=0
Divide each term by 25 and simplify.
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Divide each term in 25(x+4)2=0 by 25.
25(x+4)225=025
Cancel the common factor of 25.
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Cancel the common factor.
25(x+4)225=025
Divide (x+4)2 by 1.
(x+4)2=025
(x+4)2=025
Divide 0 by 25.
(x+4)2=0
(x+4)2=0
Set the x+4 equal to 0.
x+4=0
Subtract 4 from both sides of the equation.
x=-4
x=-4
Solve Using the Square Root Property x^2+((4x+25)/3)^2=25

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