What is x if (4x+3)^2=7?

3 Answers
Mar 15, 2018

(4x+3)^2=7

16x^2+24x+9-7=0

16x^2+24x+2=0

8x^2+12x+1=0

=((-12)+-sqrt((12^2)-4(8*1)))/(2*8)

As the quadratic formula says, from here on I leave you

Mar 15, 2018

x=(-3+-sqrt7)/"4"

Explanation:

First we expand the left hand side of the equation, by multiplying
(4x+3)(4x+3)=7

Giving us
16x^2+12x+12x+9=7

Now we get all terms to one side and combine
16x^2+24x+2=0

Now we can divide all by the constant 2, giving us
2(8x^2+12x+1)=0

Now we can divide 2 on both sides, should look like this
2/2(8x^2+12x+1)=0/2

Which simplifies to
8x^2+12x+1=0

Now this does not factor, we have to use the Quadratic Formula which is,
Quadratic Formula is
(-b +- sqrt(b^2-4ac))/"2a"

Where
a=8
b=12
c=1

Now we just plug it in
(-(12)+-sqrt(12^2-4(8)(1)))/"2(8)"

You can split this up like so
-(12)/"2(8)"+-(sqrt(12^2-4(8)(1)))/"2(8)"

After multipying and combining like terms we get
-(12)/16+-sqrt(144-32)/"16"

This then becomes
-3/4+-sqrt(112)/16

-3/4+-(sqrt(16)*sqrt(7))/16

-3/4+-(4*sqrt(7))/16

-3/4+-sqrt7/4

They have common denominators so we can have this
x=(-3+-sqrt7)/4

Mar 15, 2018

x = frac(- 3 pm sqrt(7))(4)

Explanation:

We have: (4x + 3)^(2) = 7

This problem can be done without the use of the quadratic formula.

Let's take the square root of both sides of the equation:

Rightarrow 4x + 3 = pm sqrt(7)

Subtracting 3 from both sides:

Rightarrow 4x = - 3 pm sqrt(7)

Dividing both sides by 4:

therefore x = frac(- 3 pm sqrt(7))(4)