Find a positive number that equals 42 when added to it's square

if the number is x, then

the positive number, when added to its square (remember, its=posessive and it's is a constraction), equals 42

this can be writen as

perfect, we need to solve by making one side 0 and then factoring since if ab=0, we can assume and solve for a and b by saying that a=0 and b=0

minus 42 from both sides

now, either use the quadratic formula or complete the square or factor

I will factor

find what 2 numbers multiply to get -42 and add to get 1 (since the linear coefient is 1 and the constant is -42)

those numbers are -6 and 7

factor

set each to 0

x-6=0

x=6

x+7=0

x=-7, false since we wanted a positive number

the number is 6

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

step-by-step explanation:

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