<span>x^2 + 15x + 56.25 = 105.25
"Completing the square" is one of many different techniques for solving a quadratic equation. What you do is add a constant to both sides of the equation such that the lefthand side can be factored into the form a(x+d)^2. For instance, squaring (X+D) = X^2 + 2DX + D^2. Notice the 2DX term. That is the same term as the 15x term in the problem. So 2D = 15, D = 7.5. And D^2 = 7.5^2 = 56.25.
So we have
x^2 + 15x + 56.25 = 49 + 56.25
Which is
x^2 + 15x + 56.25 = 105.25
Which is the answer desired.
Now the rest of this is going beyond the answer. Namely, it's answering the question "Why does complementing the square help?"
Well, we know that the left hand side of the equation can now be written as
(x+7.5)^2 = 105.25
Now take the square root of each side
(x+7.5) = sqrt(105.25)
And let's use both the positive and negative square roots.
So
x+7.5 = 10.25914226
and
x+7.5 = -10.25914226
And let's find X.
x+7.5 = 10.25914226
x = 2.759142264
x+7.5 = -10.25914226
x = -17.75914226
So the roots for x^2 + 15x - 49 is 2.759142264, and -17.75914226</span>
Answer:
30,290,000 people
Step-by-step explanation:
The question is asking if the trend continues from the PREVIOUS year, so we would find the 30% of 23,300,000
23,300,000/100 = 233,000 = 1%
233,000 x 30 = 6,990,000
23,300,000 = 6,990,000 = 30,290,000
$20 / 8 dessert dishes = $2.50
The cost of each dish is $2.50.
Answer: x= 34
Step-by-step explanation:
Given: The measurement of the angles of the quadrilateral are as
First angle=88°
Second angle=108°
Third angle= 2x°
Forth angle =(3x-6)°
Now, The interior angles formed by the sides of a quadrilateral have measures that sum to 360°.
Therefore,
Answer:
The first step of factorising an expression is to 'take out' any common factors which the terms have. So if you were asked to factorise x² + x, since x goes into both terms, you would write x(x + 1) . This video shows you how to solve a quadratic equation by factoring.
Step-by-step explanation:
