For what value of c is 36x²+6x+c a perfect square?

x=0

x=−0.166667

Step-by-step explanation:

Solution by completing the square for:

36x2+6x+0=0

Eliminate terms with 0 to get:

36x2+6x=0

a≠1 so divide through by 36

3636x2+636x=036

which gives us

x2+16x=0

Take half of the x term and square it

[16⋅12]2=1144

then add the result to both sides

x2+16x+1144=+0+1144

Rewrite the perfect square on the left

(x+112)2=+0+1144

and combine terms on the right

(x+112)2=1144

Take the square root of both sides

x+112=±1144−−−−√

Simplify the Radical term (0):

x+112=±112

Isolate the x on the left side and

solve for x (1)

x=−112±112

therefore (3)

x=−112+112

x=−112−112

which becomes

x=0

x=−0.166667

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6