11. Find the solutions of x^2-x-30 = 0. Please give a walkthrough/step by step I am trying to learn how to do it!

To find the solutions of quadratic equation, there are two ways to do which are:

Step 1

- Factor the expression.

To factor the expression, refer below:

For bx and ax, both can be common-factored. Therefore

From the above, we conclude that:

From the expression, 30 comes from 5×6 and when 5-6 = -1. Therefore, a can be 5 and b can be 6.

Because in the middle term, it is -x which is negative, we have to let the highest number become negative.

From the factored expression:

Then we replace the standard equation with factored form.

For this part, we solve like a linear equation where we isolate x. Just think you are solving two linear equations!

Hence

Therefore, the solutions are x = -5, 6.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)