Solving the following quadratic equation by factoring. x^{2}=4x+5

smismSitlougsyy

smismSitlougsyy

Answered question

2021-12-06

Solving the following quadratic equation by factoring.
x2=4x+5

Answer & Explanation

James Obrien

James Obrien

Beginner2021-12-07Added 16 answers

Step 1
We have to solve the quadratic equation by factorization and we also have to check the answer where quadratic equation is:
x2=4x+5
Rewriting the quadratic equation,
x2=4x+5
x24x5=0
Now solving by factorization of middle term splitting method, we get
x24x5=0
x25x+x5=0
x(x-5)+1(x-5)=0
(x-5)(x+1)=0
Either,
x-5=0
x=5
or,
x+1=0
x=-1
Hence, solutions of the quadratic equation are x=-1, 5.
Step 2
Checking the answer:
Putting x=-1 into the quadratic equation, we get
x24x5=0
(1)24(1)5=0
1+4-5=0
5-5=0
0=0
Which is satisfying the given equation.
Hence, x=-1 is the correct answer.
Putting x=5 into the quadratic equation, we get
524×55=0
25-20-5=0
5-5=0
0=0
Which is satisfying the given equation.
Hence, x=5 is the correct answer.
Both solution are correct.

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