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Anonymous asked in Science & MathematicsMathematics · 1 month ago

# Help me solve this quadrstic equation?  ?

Update:

Update 2:

Thank you so much.  I wish i could award best answer to all of you.  It helped me alot😊 Relevance

3.(4x + 1)² - 1 = 11

3.(4x + 1)² = 12

(4x + 1)² = 4

4x + 1 = ± 2

4x = - 1 ± 2

x = (- 1 ± 2)/4

x₁ = (- 1 + 2)/4 = 1/4

x₂ = (- 1 ± 2)/4 = - 3/4

• Your goal is to find values of the variable x. So, you know when you see an equation with a squared term like this you're going to have to isolate the squared term on one side of the equation so you can take it's square and get to the x-term. So, let's get all of the multipliers and additions and subtractions to the right side of the equality sign.

3(4x +1)^2 -1 = 11  So, add 1 to both sides of the equation to get rid of the -1 on the right side.

3(4x +1)^2 =12  Now, divide both sides by 3 to get rid of the 3 on the right side.(4x+2)^2 =4 Now take the square root of both sides. (To take the square root of the right side, just eliminate the exponent, and the right side is +-2

4x +1 = +-2

4x = -1+-2       (Subtract 1 from both sides.)

x =(-1+-2)/4

So the answers are -3/4 and 1/4

Hope this helps.

• 3(4x + 1)^2 - 1 = 11

3(16x^2 + 8x + 1) - 1 = 11

48x^2 + 24x + 3 - 1 = 11

48x^2 + 24x + 2 - 11 = 0

48x^2 + 24x - 9 = 0

16x^2 + 8x - 3 = 0

(4x - 1)(4x + 3) = 0

4x - 1 = 0, 4x + 3 = 0

x = 1/4, x = - 3/4

•  3(4x + 1)^2 - 1 = 11

(4x + 1)^2 = 4

(4x + 1)^2 - 2^2 = 0

(4x + 3)((4x - 1) = 0

Solutions:

x = -3/4

x = 1/4

• 48x^2+24x-9=0

x= -3/4

x=1/4

• 3(4x + 1)^2 - 1 = 11

Square up the brackets

3(16x^2 + 8x + 1) - 1 = 11

Multiply the brackets by '3'

48x^2 + 24x + 3 - 1 = 11

Equate everything to the 'zero'

48x^2 + 24x - 9 = 0

Apply the Quadratic Eq'n , which is

x = { - b +/- sqrt[b^2 - 4ac]} / 2a

where

a = 48

b = 24

c = -9

Hence x = { - 24 +/-sqrt[(24)^2 - 4(48)(-9)]} / 2(48)

x = { -24 +/-sqrt[576 + 1728]} / 96

x = { - 24 +/- sqrt[ 2304]} / 96

x = - 24 +/- 48] / 96

x = -72 / 96 = - 3/4

x = 24/96 = 1/4

Done!!!!

• You solve almost any algebra equation the same way: do the same thing to both sides until you are left with x alone on one side.

Let's say you have two expressions that are equal. It doesn't matter what they are, so let's call them ζ and Φ. Then you add 2 to each of them, or you multiply each by 17, or square them, or take the tangent of each. You're doing whatever operation to by definition the same number on both sides, therefore you end up with the same number on both sides. If ζ = Φ then tan(17(ζ+2)^2)  = tan(17(Φ+2)^2).

There is one thing to watch out for. A positive number has two square roots: one positive and the other negative. Thus if you take the square root of both sides of x^2 = 9, you get x = ±3. Alternatively you could take only the positive square root, while remembering that you don't know whether x is negative: |x| = 3.

That's why a quadratic equation can end up with two different solutions.

Now take a look at your quadratic equation. There's only one x, so do operations that get rid of everything else around the x. The first step is to add 1. Since we add 1 to both sides of the equation, this turns it into

3(4x+1)^2 = 12

Then divide both sides by 3, and so on.

• 3(4x+1)^2 -1 = 11

3 [(4x+1)(4x+1)] -1 = 11

3(16x^2 + 8x + 1) -1 = 11

48x^2 +24x +3 -1 = 11

48x^2 +24x +2 = 11

48x^2 +24x -9 = 0

Each factor is divisible by 3, so:

16x^2 + 8x -3 = 0

I'll let you continue the derivation from here.  Use the quadratic formula.

• 3(4x+1)² – 1 = 11

3(4x+1)² = 11 + 1

3(16x² + 8x + 1) = 12

16x² + 8x + 1 = 4

16x² + 8x – 3 = 0

to solve ax² + bx + c = 0

x = [–b ± √(b²–4ac)] / 2a

x = [–8 ± √(64+4•48)] / 32

x = [–8 ± √256] / 32

x = [–8 ± 16] / 32

x = –24/32, +8/32

x = –3/4, +1/4

check

3(4x+1)² – 1 = 11

3(4(–3/4)+1)² – 1 = 11

3(–3+1)² – 1 = 11

3(–2)² – 1 = 11

3•4 – 1 = 11

12 – 1 = 11

ok

3(4(1/4)+1)² – 1 = 11

3(1+1)² – 1 = 11

3•4 – 1 = 11

ok

• You can do one of two things:

expand it to a polynomial and use quadratic equation, or:

just unwind the binomial-squared information to get to the variable.

You are likely expected to do the latter:

3(4x + 1)² - 1 = 11

3(4x + 1)² = 12

Divide both sides by 3:

(4x + 1)² = 4

Square root of both sides:

4x + 1 = ±2

Subtract 1 from both sides:

4x = -1 ± 2

Divide both sides by 4:

x = (-1 ± 2) / 4

Split up the ± into two solutions and simplify each:

x = (-1 - 2) / 4 and x = (-1 + 2) / 4

x = -3/4 and x = 1/4

• Add 1 to both sides

3 * (4x + 1)^2 - 1 + 1 = 11 + 1

3 * (4x + 1)^2 + 0 = 12

3 * (4x + 1)^2 = 12

Divide both sides by 3

3 * (4x + 1)^2 / 3 = 12 / 3

1 * (4x + 1)^2 = 4

(4x + 1)^2 = 4

Takes the square root of both sides

((4x + 1)^2)^(1/2) = 4^(1/2)

(4x + 1)^(2/2) = -2 , 2

(4x + 1)^1 = -2 , 2

4x + 1 = -2 , 2

Subtract 1 from both sides

4x + 1 - 1 = -2 - 1 , 2 - 1

4x + 0 = -3 , 1

4x = -3 , 1

Divide both sides by 4

4x/4 = -3/4 , 1/4

1 * x = -3/4 , 1/4

x = -3/4 , 1/4