Solve the equation. x=4+\sqrt{4x-19}

Jerold

Jerold

Answered question

2021-10-01

Solve the equation.
x=4+4x19

Answer & Explanation

Sadie Eaton

Sadie Eaton

Skilled2021-10-02Added 104 answers

Step 1
We have to solve the equation:
x=4+4x19
Rewriting the equation,
x=4+4x19
x4=4x19
Squaring both sides ( when we square then we must have to check the solution at the end),
(x4)2=(4x19)2
(x)22(x)(4)+(4)2=(4x19)
x28x+16=4x19
x28x4x+16+19=0
x212x+35=0
Solving the equation by factorization of middle term splitting method,
x212x+35=0
x27x5x+35=0
x(x-7)(x-5)=0
Therefore,
x-7=0
x=7
and,
x-5=0
x=5
Hence, solutions of the equation are x=5, 7.
Step 2
Now checking the answer by putting into the equation:
Putting x=5,
x=4+4x19
5=4+4×519
=4+2019
=4+1
5=5
Hence, this solution is correct.
Putting x=7,
x=4+4x19
7=4+4×719
=4+2819
=4+9
=4+3
7=7
Hence, both solutions are correct.

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