Answer:x=31.4919
Step-by-step explanation:
Step1:isolate a square root on the left hand side√x+3=√2x-1-2
Step2:eliminate the radicals on the left hand side
Raise both sides to the second power
√x+3)^2=(√2x-1-2)^2
After squaring
x+3=2x-1+4-4-4√2x-1
Step3:get the remaining radicals by itself
x+3=2x-1+4-4√2x-1
Isolate radical on the left hand side
4√2x-1=-x-3+2x-1+4
4√2x-1=x
Step4:eliminate the radicals on the left hand side
Raise both side to the second power
(4√2x-1)^2=x^2
After squaring
32x-16=x^2
Step 5:solve the quadratic equation
x^2-32x-16
This equation has two real roots
x1=32+√960/2=31.4919
x2=32-√960/2=0.5081
Step6:check that the first solution is correct
Put in 31.4919 for x
√31.4919+3=√2•31.4919-1-2
√34.492=5.873
x=31.4919
Step7:check that the second solution is correct
√x+3=√2x-1-2
Put in 0.5081 for x
√0.5081+3=√2•0.5081-1-2
√3.508=-1.873
1.873#-1.873
One solution was found
x=31.4919
