Question

Solve a^2 + 2a − 3 = 0

Answer 1

Answer:  a= -3

               a= 1

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Answer 2

Solving Quadratic Equations by Completing the Square

Answer:

$a = 1$ and $a = -3$

Step-by-step explanation:

Solving by Completing the Square:

$a^2 +2a -3 = 0 \\ a^2 +2a -3 +3 = 0 +3 \\ a^2 +2a = 3 \\ a^2 +2a +1 = 3 +1 \\ (a +1)^2 = 4 \\ \sqrt{(a +1)^2} = \pm \sqrt{4} \\ a +1 = \pm 2$

Solving for $a$ from the positive root:

$a +1 = 2 \\ a +1 -1 = 2 -1 \\ a = 1$

Solving for $a$ from the negative root:

$a +1 = -2 \\ a +1 -1 = -2 -1 \\ a = -3$

The solutions are $a = 1$ and $a = -3$