In the first few steps for deriving the quadratic formula left side of the equation due to the distributive property for balancing the equation.
<h3>What is quadratic equation?</h3>
A quadratic equation is the equation in which the highest power of the variable is two.
Here, The first few steps in deriving the quadratic formula are shown in the table.
Use the substitution property of equality to solve it further,
-c=-ax² +bx
Now factor out the term a, to solve further as,
- c = a (x² + b/a x)
for half of the b value and square it to determine the constant of the perfect square trinomial as,
(b/2a)² = b²/4a²
Now the distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.
-c + b²/4a² = a(x² + b/a x + b²/4a² )
Thus, the distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.
Learn more about Quadratic equation from:
brainly.com/question/14336752
#SPJ1
Answer:
-20x+8
Step-by-step explanation:
Step 1: rearrange the equation
16x^2 - 3x^2 - 7x - 13x +8
Step 2: solve the equation
16x^2 - 3x^2 = 13x^2
-7x - 13x = -20x
(the +8 will stay the same)
so when we put it all together it gives us
13x^2 - 20x + 8
Answer:
- equation: (x-3) +(x-1) +(x+1) +(x+3) = -72
- values: -21, -19, -17, -15
Step-by-step explanation:
When dealing with consecutive integers, it often simplifies the problem to work with their average value. We know the average value of the integers in this problem is the even integer between the middle two. We can call it x, and write the equation ...
(x-3) +(x-1) +(x+1) +(x+3) = -72
This simplifies to ...
4x = -72 . . . . . . . we knew this before we wrote the above equation, since the sum of 4 numbers is 4 times their average.
x = -18 . . . . . . . . the middle number of the sequence
So, the numbers are:
- -18-3 = -21
- -18-1 = -19
- -18+1 = -17
- -18+3 = -15
_____
A more conventional approach is to define the variable as the integer at one end or the other of the sequence. If we make it be the lowest number, then the equation is ...
(x) +(x +2) +(x +4) +(x +6) = -72
and that simplifies to ...
4x +12 = -72 . . . . . collect terms
4x = -84 . . . . . . . . subtract 12
x = -21 . . . . . . . . . . divide by 4
Now, the other three numbers are found by adding 2, 4, and 6 to this one.
For the first one, to find the missing fraction, add the first two fractions and subtract that from the last fraction. For the second question, subtract the first two fractions then add that to the last fraction. Hope this helps.
