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+2x−3=3−3 Simplify 5x2+2x−3=0 Solve with the quadratic formula x1, 2=−b±b2−4ac2a For a=5, b=2, c=-3 x1, 2=−2±22−4×5(−3)2×5 22−4×5(−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=−2−82×5 x=−2+82×5:35 x=−2−82×5: −1 The solutions to the quadratic equation are: x=35, x=−1

Expert answers to "To solve: x(5x+2)=3"

High School
Algebra
Algebra I
Quadratic function and equation

Monique Slaughter

Answered question

2021-12-29

To solve:

x (5 x + 2) = 3

Answer & Explanation

Alex Sheppard

Beginner2021-12-30Added 36 answers

Step 1
Given:

x (5 x + 2) = 3

By distributive property,

x (5 x + 2) = x \times 5 x + x \times 2

x (5 x + 2) = 5 x^{2} + 2 x

Replace

x (5 x + 2)

with

5 x^{2} + 2 x

To solve

5 x^{2} + 2 x = 3

Subtract 3 on both sides,

5 x^{2} + 2 x - 3 = 3 - 3

5 x^{2} + 2 x - 3 = 0

To solve,

5 x^{2} + 2 x - 3 = 0

Split the middle term

+ 2 x as + 5 x and - 3 x

Replace

+ 2 x with + 5 x - 3 x in 5 x^{2} + 2 x - 3 = 0

5 x^{2} + 5 x - 3 x - 3 = 0

The above equation can be written as

5 x \times x + 1 \times 5 x - 3 \times x - 3 \times 1

Apply distributive property for first two terms and last two terms,

5 x \times x + 1 \times 5 x - 3 \times x - 3 \times 1 = 5 x (x + 1) - 3 (x + 1)

Again apply distributive property for

5 x (x + 1) - 3 (x + 1)

5 x (x + 1) - 3 (x + 1) = (5 x - 3) (x + 1)

So the factors are

(5 x - 3)

and

(x + 1)

5 x^{2} + 2 x - 3 = (5 x - 3) (x + 1)

To find the value of x,
Take

x + 1 = 0

Subtract 1 on both sides,

x + 1 - 1 = 0 - 1

x = - 1

Take

5 x - 3 = 0

Add 3 on both sides,

5 x - 3 + 3 = 0 + 3

5 x = 3

Divide by 5 on both sides,

\frac{5 x}{5} = \frac{3}{5}

x = \frac{3}{5}

So, the values of x are

\frac{3}{5}

and -1

Annie Gonzalez

Beginner2021-12-31Added 41 answers

Lets

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: $a^{b} \times a^{c} = a^{b + c}$ $x \times x = x^{1 + 1}$
$= 5 x^{1 + 1}$
Add the numbers: 1+1=2
$= 5 x^{2}$
$= 5 x^{2} + 2 x$
$5 x^{2} + 2 x = 3$
Subtract 3 from both sides
$5 x^{2} + 2 x - 3 = 3 - 3$
Simplify
$5 x^{2} + 2 x - 3 = 0$
Solve with the quadratic formula
$x_{1, 2} = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
For a=5, b=2, c=-3
$x_{1, 2} = \frac{- 2 \pm \sqrt{2^{2} - 4 \times 5 (- 3)}}{2 \times 5}$
$\sqrt{2^{2} - 4 \times 5 (- 3)}$
Apply rule -(-a)=a
$= \sqrt{2^{2} + 4 \times 5 \times 3}$
Multiply the numbers: $4 \times 5 \times 3 = 60$
$= \sqrt{2^{2} + 60}$
$2^{2} = 4$
$= \sqrt{4 + 60}$
Add the numbers: $4 + 60 = 64$
$= \sqrt{64}$
Factor the number: $64 = 8^{2}$
$= \sqrt{8^{2}}$
Apply radical rule: $\sqrt[n]{a^{n}} = a$
$\sqrt{8^{2}} = 8$
$= 8$
$x_{1, 2} = \frac{- 2 \pm 8}{2 \times 5}$
Separate the solutions
$x_{1} = \frac{- 2 + 8}{2 \times 5}, x_{2} = \frac{- 2 - 8}{2 \times 5}$
$x = \frac{- 2 + 8}{2 \times 5} : \frac{3}{5}$
$x = \frac{- 2 - 8}{2 \times 5} : - 1$
The solutions to the quadratic equation are:
$x = \frac{3}{5}, x = - 1$

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