^{2}

^{2}+36x +81

(2x+ 6)2= (2x+9)^{2}

x^2 4x224x+36+4^{2}+36x +81

Tutors, sign in to answer this question.

So I'll do the problem two ways:

1.

(2x+6)^2 = (2x+9)^2

Take square root of both sides (N.B.: √(k^2) == |k| ):

|2x+6| = |2x+9|

2x+6 = ±(2x+9)

case 1: 2x+6 = +(2x+9)

6 = 9 is never true so there is no solution for this case.

case 2: 2x+6 = -(2x+9)

2x + 6 = -2x - 9

4x = -15

x = -15/4

check: (2(-15/4)+ 6)^2 =? (2(-15/4)+9)^2

(-15/2+12/2)^2 =? (-15/2+18/2)^2

(-3/2)^2 =? (3/2)^2

9/4 = 9/4 √ , so -15/4 is the only solution to problem 1.

2.

2*(2x+6) = (2x+9)^2

4x + 12 = 4x^2 + 36x + 81

0 = 4x^2 + 32x + 69

Use Quadratic Formula:

x = (-32 ± √(32^2-4(4)(69)))/(2(4))

x = -4 ± (√((32/4)^2-4(4)(69)/4^2))/2

x = -4 ± (√(8^2-69))/2

x = -4 ± (√(64-69))/2

x = -4 ± (i√(5))/2

check:

2*(2(-4 ± (i√(5))/2) + 6) =? (2(-4 ± (i√(5))/2) + 9)^2

2*(-8 ± i√(5) + 6) =? (-8 ± i√(5) + 9)^2

2*(-2 ± i√(5)) =? (1 ± i√(5))^2

-4 ± 2i√(5) =? 1 ± 2i√(5) - 5

-4 ± 2i√(5) = -4 ± 2i√(5) √

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.