Solve the equation. x+\sqrt{5x+19}=-1

parthe0o

parthe0o

Answered question

2021-11-19

Solve the equation.
x+5x+19=1

Answer & Explanation

Vincent Diaz

Vincent Diaz

Beginner2021-11-20Added 19 answers

Given,
x+5x+19=1
Step 2
On simplification, we get
5x+19=1x
(5x+19)2=(1x)2 [Squaring on both sides]
5x+19=1+2x+x2
x23x18=0
x26x+3x18=0
x(x6)+3(x6)=0
(x6)(x+3)=0
x6=0 or x+3=0
x=6 or x=3
But the given equation does not satisfy when x=6.
Therefore solution is,
x=−3
Keith Dooley

Keith Dooley

Beginner2021-11-21Added 14 answers

Step 1: Isolate the square root on the left hand side
Original equation
x+5x+19=1
Isolate
5x+19=x1
Step 2: Eliminate the radical on the left hand side
Raise both sides to the second power
(5x+19)2=(x1)2
After squaring
5x+19=x2+2x+1
Step 3: Solve the quadratic equation
Rearranged equation
x23x18=0
This equation has two rational roots:
{x1, x2}={6, -3}
Step 4: Check that the first solution is correct
Original equation, root isolated
5x+19=x1
Plug in 6 for x
5(6)+19=(6)1
Simplify
49=7
Solution does not check
77
Step 5: Check that the second solution is correct
Original equation, root isolated
5x+19=x1
Plug in -3 for x
5(3)+19=(3)1
Simplify
4=2
Solution is:
x = -3

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