(A)Write the equation in standard form and calculate its discriminant. (B)Solve the equation by using the quadratic formula. (C)After solving the equation, write it in factored form. 1/8x^2=x-5/2 Please help!!!!! :(

1/8x^2=x-5/2

multiply each term by 8

x^2 = 8x - 20
x^2 - 8x + 20 = 0

You MUST know how to do the rest

betting not :)

1x^2 -8x +20 = 0

if a =1, b=- 8 and c=20
and the discriminant is b^2 - 4ac sub in your values : )

Sure, I can help you solve the equation and explain each step.

(A) To write the equation in standard form, we need to move all the terms to the left side of the equation and set it equal to zero.

1/8x^2 = x - 5/2

Multiply both sides of the equation by 8 to eliminate the fraction:

8 * (1/8x^2) = 8 * (x - 5/2)

x^2 = 8x - 20

Now, let's write the equation in standard form:

x^2 - 8x + 20 = 0

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Next, we need to calculate the discriminant. The discriminant is denoted by the symbol Δ and is calculated using the formula:

Δ = b^2 - 4ac

For our equation, the values of a, b, and c are:

a = 1, b = -8, c = 20

Substituting these values into the formula:

Δ = (-8)^2 - 4(1)(20)

Δ = 64 - 80

Δ = -16

(B) Now, let's solve the equation using the quadratic formula:

The quadratic formula is given by:

x = (-b ± √Δ) / (2a)

Plugging in the values from our equation:

x = (-(-8) ± √(-16)) / (2 * 1)

x = (8 ± √(-16)) / 2

Since the discriminant is negative, we have the square root of a negative number, which means that the equation has no real solutions. The graph of the equation would be a parabola that does not intersect the x-axis.

(C) Since the equation has no real solutions, it cannot be factored.