Solve by completing the square. X^2+8x=-15

Question

Solve by completing the square.  X^2+8x=-15

Answer 1

x^2 + 8x = -15

 

x^2 + 8x + 15 = 0

 

(x + a)^2 = x^2 + 2ax + a^2, so if we can make a pattern like the right side we can replace it with a pattern like the left side.

 

x^2 +     8x           + 0          + 15 = 0

                    <----------------->

x^2 + 2(4)x + (4)^2 - (4)^2 + 15 = 0

<----------------------->

        (x + 4)^2         - 16      + 15 = 0

 

(x + 4)^2 = 1

 

Take square root of both sides, noting that √(r^2) == |r|:

 

|x + 4| = √(1)

 

x + 4 = ± 1

 

x = -4 ± 1

 

x = -5, -3

 

check:

 

(-5)^2 + 8(-5) =? -15

25 - 40 =? -15

-15 = -15 √

 

(-3)^2 + 8(-3) =? -15

9 - 24 =? -15

-15 = -15 √

Answer 2

Hi Abby;

X^2+8x=-15

Let's work with...

x²+8x

This is a parabola...

Ax²+Bx+C

The formula to establish C such that the equation is a perfect square is...

(B/2)²

(8/2)²

16

x²+8x+16

(x+4)(x+4)

Let's FOIL...

FIRST...(x)(x)=x²

OUTER...(x)(4)=4x

INNER...(4)(x)=4x

LAST...(4)(4)=16

x²+4x+4x+16

x²+8x+16

The equation we want is...

X^2+8x=-15

x²+8x+15=0

15=16-1

x²+8x+16-1=0

x²+8x+16=1

(x+4)²=1

Square-root both sides...

x+4=1.......x+4=-1

x=-3...........x=-5