<em>So</em><em> </em><em>the</em><em> </em><em>last</em><em> </em><em>number</em><em> </em><em>is</em><em> </em><em>3</em><em>4</em><em>.</em>
<em>Hope</em><em> </em><em>this</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>u</em><em>.</em><em>.</em><em>.</em>
<span>Peter paid </span>84 cent in taxs
80*4=320
89*4=356
This is the range of the addition of all 4 scores.
99+80+70=249
320-249= 71
356-249= 107
[71, 100] would be the answer, unless you can get extra credit on the final.
<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: (x+2)*(x-4)*(x+21) = 0 has "many" solutions
Step-by-step explanation: (x+2) = 0 only has one solution.
(x+2)*(x-4) = 0 has two solutions, -2 and 4
(x+2)*(x-4)*(x+21) = 0 has three solutions, -2, 4, and -21, etc
If "many" means more than three, then add another (x+XX) term. A quadratic equation generally has two solutions.
