Question

Solve 3(a+1)^2 +2=11 with 2 different methods

Answer 1

Answer:

$a = - 1 - \sqrt{3} \: or \: a = - 1 + \sqrt{3}$

Step-by-step explanation:

We want to solve

$3 {(a + 1)}^{2} + 2 = 11$

with two different methods.

Subtract 2 from both sides:

$3 {(a + 1)}^{2} = 11 - 2 \\ 3 {(a + 1)}^{2} = 9$

Divide through by 3

${(a + 1)}^{2} = 3$

Take square root:

$a + 1 = \pm \sqrt{3}$

$a = - 1\pm \sqrt{3}$

$a = - 1 - \sqrt{3} \: or \: a = - 1 + \sqrt{3}$

Method 2:

The given equation is

$3 {(a + 1)}^{2} + 2 = 11$

Expand

$3( {a}^{2} + 2a + 1) + 2 = 11$

Subtract 11

$3( {a}^{2} + 2a + 1) - 9 = 0$

Divide through by 3

${a}^{2} + 2a + 1 - 3 = 0 \\ {a}^{2} + 2a - 2 = 0$

Use the quadratic formula:

$a = \frac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 1 \times - 2} }{2 \times 1}$

$a = \frac{ - 2 \pm \sqrt{ 12} }{2}$

$a = \frac{ - 2 \pm2 \sqrt{3} }{2}$

$a = - 1 \pm\sqrt{3}$

$a = - 1 - \sqrt{3} \: or \: a = - 1 + \sqrt{3}$