Work out the area of this triangle. I will mark you as brainliest, please help quick.
1 answer:
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Answer:
<u>x = 5 or 25</u>
Step-by-step explanation:
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 <u>dividing the 'b' value </u><u>(-30)</u><u> by 2</u> (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) =
<u>x² - 30x + 225</u>
There is an <u>unwanted term</u> (the + 225, from 15²)! We only want x² - 30x, so we have to remove this term by <u>subtracting it from the left side of the equation</u>. To do this, let's set up the original equation again:
(x² - 30x + 225) <u>- 225</u> = - 125
<em>Note: </em><em>The reason why we don't have to subtract it from both sides is because the original equation is </em><em>x² - 30x = - 125</em><em>, and so we must make sure the left hand side is still equal to </em><em>x² - 30x</em><em>.</em>
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 <u>both sides</u> 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
<u>x = 25</u> This is our first solution.
2. x = -10 + 15 <- add 15 to both sides again
<u>x = 5</u> This is our other solution.
<u>So our two solutions are x = 5 and x = 25!</u>
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.
To apply the quadratic formula, the right side must be equal to 0.
Now you can apply the quadratic formula
to find the solution for w.
(The quadratic formula is highly unnecessary in this problem, however. You could easily divide all values by 2 to get w²-14w+49=0, which factors into (w-7)²=0, for which 7 is the only solution which puts a factor of the quadratic equal to 0.)
Now you can apply the quadratic formula
(The quadratic formula is highly unnecessary in this problem, however. You could easily divide all values by 2 to get w²-14w+49=0, which factors into (w-7)²=0, for which 7 is the only solution which puts a factor of the quadratic equal to 0.)