Math Editor

√x2+3x+9​ + √x2+3x+4​ =5

Let y=x2+3x

√y+9​+√y+4​=5

√y+9​=5−√y+4​

Taking 'square' both sides

(√y+9​)2=(5−√y+4​)2

y+9=(5)2−2(5)(√y+4​)+(√y+4​)2

y+9=25−10√y+4​+y+4

10√y+4​=25+y+4−y−9

10√y+4​=20√y+4​=2Taking square both sides(√y+4​)2=(2)2y+4=4y=4−4y=0Restoring the value of yx2+3x=0x(x+3)=0x=0 x+3=0x=−3CheckFor x=0√(0)2+3(0)+9​+√(0)2+3(0)+4​=5√0+0+9​+√0+0+4​=5√9+√4=53+2=55=5For x=−3√(−3)2+3(−3)+9​+√(−3)2+3(−3)+4​=5√0+0+9​+√0+0+4​=5√9+√4=53+2=55=5​