How do you solve sqrt (3x + 4) + x = 8√3x+4+x=8?

2 Answers
Somebody N.
Mar 23, 2018

color(blue)(x=16)x=16

color(blue)(x=4)x=4

Explanation:

sqrt(3x+4)+x=8√3x+4+x=8

Subtract xx from both sides:

sqrt(3x+4)=8-x√3x+4=8−x

Square both sides:

3x+4=(8-x)^23x+4=(8−x)2

Expand the bracket:

3x+4=64-16x+x^23x+4=64−16x+x2

Collect like terms:

x^2-19x+60=0x2−19x+60=0

Factor:

x^2-15x-4x+60x2−15x−4x+60

x(x-15)-4(x-15)x(x−15)−4(x−15)

(x-15){x-4}(x−15){x−4}

(x-16)(x-4)=0(x−16)(x−4)=0

x-16=0=>color(blue)(x=16)x−16=0⇒x=16

x-4=0=>color(blue)(x=4)x−4=0⇒x=4

Binayaka C.
Mar 23, 2018

Solution: x=4 , x=15x=4,x=15

Explanation:

sqrt(3x+4)+x =8 or sqrt(3x+4) =8-x √3x+4+x=8or√3x+4=8−x Squaring both sides

we get, 3x+4 = (8-x)^2 or 3x+4 = x^2-16x+643x+4=(8−x)2or3x+4=x2−16x+64 or

x^2-16x+64-3x-4=0 or x^2-19x+60=0 x2−16x+64−3x−4=0orx2−19x+60=0 or

x^2-15x-4x+60=0 x2−15x−4x+60=0 or

x(x-15)-4(x-15)=0 or (x-15)(x-4)=0 :.

Either x-15=0 :. x=15 , or x-4=0 :. x=4

Check : sqrt(3*4+4)+4 =8 or sqrt16+4=8or 8=8

sqrt(3*15+4)+15 =8 or sqrt49+15=8 or -7+15=8

Solution: x=4 , x=15 [Ans]

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