Derive the quadratic formula from the standard form (ax² + bx + c = 0) of a quadratic equation by
following the steps below.
1. divide all terms in the equation by a.
2. subtract the constant (the term without an x) from both sides.
3. add a constant (in terms of a and b) that will complete the square.
4. take the square root of both sides of the equation.
5. solve for x.

1. Divide all terms by a:

2. Subtract the constant (which is c/a):

3. Complete the square, then add the constant to both sides:

(now add the constant in terms of a and b)

(now simplify the fractions on the right side)

(now just put the b^2 in front)

4. Square root both sides and simplify the right side:

(you can square root the bottom bit of the fraction fully)

5. Now just solve for x:

(now simplify)

(note: it should be a plus or minus sign infront of the squareroot, not just a plus sign -it's just that i can't write it in )

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If you have any questions, feel free to ask.

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it