To solve: x(5x+2)=3

Monique Slaughter

Monique Slaughter

Answered question

2021-12-29

To solve:
x(5x+2)=3

Answer & Explanation

Alex Sheppard

Alex Sheppard

Beginner2021-12-30Added 36 answers

Step 1
Given: x(5x+2)=3
By distributive property,
x(5x+2)=x×5x+x×2
x(5x+2)=5x2+2x
Replace x(5x+2) with 5x2+2x
To solve 5x2+2x=3
Subtract 3 on both sides,
5x2+2x3=33
5x2+2x3=0
To solve, 5x2+2x3=0
Split the middle term +2x as +5x and 3x
Replace +2x with +5x3x in 5x2+2x3=0
5x2+5x3x3=0
The above equation can be written as 5x×x+1×5x3×x3×1
Apply distributive property for first two terms and last two terms,
5x×x+1×5x3×x3×1=5x(x+1)3(x+1)
Again apply distributive property for 5x(x+1)3(x+1)
5x(x+1)3(x+1)=(5x3)(x+1)
So the factors are (5x3) and (x+1)
5x2+2x3=(5x3)(x+1)
To find the value of x,
Take x+1=0
Subtract 1 on both sides,
x+11=01
x=1
Take 5x3=0
Add 3 on both sides,
5x3+3=0+3
5x=3
Divide by 5 on both sides,
5x5=35
x=35
So, the values of x are 35 and -1
Annie Gonzalez

Annie Gonzalez

Beginner2021-12-31Added 41 answers

Lets
karton

karton

Expert2022-01-10Added 613 answers

Step 1
Given: x(5x+2)=3
Expand:
Apply the distributive law: a(b+c)=ab+ac

a=x, b=5x, c=2

x*5x+x*2
=5x* x+2x

Apply exponent rule: ab×ac=ab+cx×x=x1+1
=5x1+1
Add the numbers: 1+1=2
=5x2
=5x2+2x
5x2+2x=3
Subtract 3 from both sides
5x2+2x3=33
Simplify
5x2+2x3=0
Solve with the quadratic formula
x1, 2=b±b24ac2a
For a=5, b=2, c=-3
x1, 2=2±224×5(3)2×5
224×5(3)
Apply rule -(-a)=a
=22+4×5×3
Multiply the numbers: 4×5×3=60
=22+60
22=4
=4+60
Add the numbers: 4+60=64
=64
Factor the number: 64=82
=82
Apply radical rule: ann=a
82=8
=8
x1, 2=2±82×5
Separate the solutions
x1=2+82×5, x2=282×5
x=2+82×5:35
x=282×5: 1
The solutions to the quadratic equation are:
x=35, x=1

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