B/2 = -7 + B multiply the two facets via 2 (*2)B/2 = 2(-7+B) simplify B = -14 + 2B subtract 2B from the two facets B (-2B) = -14 + 2B (-2B) simplify -B = -14 divide via a destructive to isolate your variable -B/- = -14/- simplify B = 14 --------------------------------------... to verify: positioned your fee for B that's 14 interior the equation the place B is located 14/2 = -7+14 7 = 7 and the solutions are a similar so that's right
Comments
Hi there! You need to remember / know the following stuff to solve this problem:
♦ √(x + y)² = (x + y) (and vice versa)
♦ (x - y)² = x² - 2xy + y² (and vice versa)
√(30x + 15) = x + 8 → Write down the equation correctly.
30x + 15 = (x + 8)² → Square both sides now.
30x + 15 = x² + 16x + 64 → Expand brackets on right side.
30x + 15 - x² - 16x - 64 = 0 → Move all terms to left side.
14x - 49 - x² = 0 → Simplify like terms.
- (x² - 14x + 49) = 0 → Leave the minus out the bracket.
- (x - 7)² = 0 → Factor by applying formula.
(x - 7)² = 0 → Multiply both sides by (- 1).
(x - 7) = 0 → Take square root of both sides.
→ x - 7 = 0
x = 0 + 7
x = 7 (solution)
Hope this helped, have a good day!
~Maths
sqrt( 30x + 15 ) = x + 8
You need to get rid of that square root, so square both sides.
( 30x + 15 )= ( x + 8 )^2
FOIL out the binomial.
30x + 15 = x^2 + 16x + 64
Bring everything together on the same side and combine like terms.
0 = x^2 - 14x + 49
You could do quadratic formula or completing the square, but the easiest way is to realize that it factors.
0 = ( x - 7 )^2
x - 7 = 0
x = 7
Square both sides
30x + 15 = x^2 + 16x + 64
x^2 - 14x + 49 = 0
(x-7)^2 = 0 , x=7
√(30x+15) = x+8
Squaring on both sides we get
30x+15 = (x+8)²
30x+15 = x² + 16x + 64
x² - 14x + 49 = 0
(x-7)² = 0
x= 7
30x+15 = (x+8)^2
x^2 -14x +49 =0
(x-7)^2 =0
x= 7
7 multiplicity of 2
square both sides
30x+15=x^2+16x+64
Get everyhting to one side
0=x^2-14x+49
Factor
0=(x-7)^2
x-7=0
x=7
the answer can't be 7!
30x+15=x+8
30x-x=8-15
29x=-7
x=-7/29
so the square root of x is : √(-7/29)
B/2 = -7 + B multiply the two facets via 2 (*2)B/2 = 2(-7+B) simplify B = -14 + 2B subtract 2B from the two facets B (-2B) = -14 + 2B (-2B) simplify -B = -14 divide via a destructive to isolate your variable -B/- = -14/- simplify B = 14 --------------------------------------... to verify: positioned your fee for B that's 14 interior the equation the place B is located 14/2 = -7+14 7 = 7 and the solutions are a similar so that's right