2. Solve the equation by completing the square. Show your work.

x^2-30x=-125

Step 1: add (b)^2
—
2
To both sides of the equation.

Step2: factor the left side of the equation. Show your work.

Step 3: take the square root of both sides of the equation from step2.

Step 4: simplify the radical and solve for x. Show your work.

35 points!!! to whoever help me this. Thank you very much

I think the method I am about to explain is slightly quicker and easier than the method in your question. This works for any 'complete the square' question.

We begin with x² - 30x = - 125.

First, we are going to factorise the left-hand side of the equation by dividing the 'b' value (-30) by 2 (you'll see why this works in a minute):

(x - 15)²

We want these brackets to multiply out to give x² - 30x, so that they equal the left-hand side of the equation. Unfortunately, if we multiply them out, we get:

(x - 15)(x - 15) =

x² - 30x + 225

There is an unwanted term (the + 225, from 15²)! We only want x² - 30x, so we have to remove this term by subtracting it from the left side of the equation. To do this, let's set up the original equation again:

(x² - 30x + 225) - 225 = - 125

Note: The reason why we don't have to subtract it from both sides is because the original equation is x² - 30x = - 125, and so we must make sure the left hand side is still equal to x² - 30x.

So now we know that (x - 15)² multiplies out to give x² - 30x +225, we can write this as (x - 15)² in our equation:

(x² - 30x + 225) - 225 = - 125

is the same as:

(x - 15)² - 225 = - 125

Now add 225 to both sides of the equation:

(x - 15)² = - 125 + 225 = 100

(x -15)² = 100

The next step is to square root both sides. Be careful here, and remember that √100 can either be 10 or -10, as (-10)² = 100. To indicate both results, write ±10 ("plus or minus 10").

√(x - 15)² = √100

x - 15 = ±10

Because, there are two possible values for the right-hand side of the equation, we need to separate our equation into two equations:

1. x - 15 = 10

and

2. x - 15 = -10

Now we solve these two simple linear equations for x:

1. x = 10 + 15 <- add 15 to both sides

x = 25 This is our first solution.

2. x = -10 + 15 <- add 15 to both sides again

x = 5 This is our other solution.

So our two solutions are x = 5 and x = 25!

I have attached the quick version of the working out for this question - that is what you would be expected to write down in a test.

poona2339 poona2339 · Answer 2 · 2022-07-21T19:11:23+02:00

x = 5 or 25

What is factorization in math?

Set up the product of binomials.
Write values for the 1st term in each binomial like that the product of the values is = to the 1st term of the expression being factored.
Find a product of 2 values that is = to the 3rd term in the expression being factored

We begin with x² - 30x = - 125.

First, we are going to factorise the left-hand side (LHS) of the equation by dividing the 'b' value (-30) by 2 (you'll see why this works in a minute):

(x - 15)²

We need these brackets to multiply out the give x² - 30x, so that they = the left-hand side (LHS) of the equation. Unfortunately, if we multiply them out, we get:

(x - 15)(x - 15) =

x² - 30x + 225

There are an unwanted term (the + 225, from 15²)! We only need x² - 30x, so we have to remove this term by subtracting this from the left side of the equation. To do this, let's set up the original equation again:

(x² - 30x + 225) - 225 = - 125

Note: The reason why we do not have to subtract this from both sides is because original equation is x² - 30x = - 125, and so we must make sure the left hand side is = to x² - 30x.

So now we know that (x - 15)² multiplies out to give x² - 30x +225, we can write this as (x - 15)² in our equation:

(x² - 30x + 225) - 225 = - 125

as the same as:

(x - 15)² - 225 = - 125

Now add 225 to both sides by the equation:

(x - 15)² = - 125 + 225 = 100

(x -15)² = 100

The next step is to square root by both sides. Be careful here, or remember that √100 can either be 10 or -10, as (-10)² = 100. To indicate both results, write ±10 ("plus or minus 10").

√(x - 15)² = √100

x - 15 = ±10

Because, there are 2possible values for the right-hand side of the equation, we need to separate this equation into 2 equations:

1. x - 15 = 10

and

2. x - 15 = -10

Now we have solve these two simple linear equations for x:

1. x = 10 + 15 <- add 15 to both sides

x = 25 This is our first solution.

2. x = -10 + 15 <- add 15 to both sides again

x = 5 This is our other answer.

Learn more about factorization here https://brainly.com/question/713325

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