COMPLETING THE SQUARE 2x^2 -4x+3=9 2. QUADRATIC FORMULA 2x^2+4x=0

2 months ago

Solution 1

Guest #3298
2 months ago
X = 3 and x = -1 are the answers for both. They are exactly the same equation.

FOR COMPLETING THE SQUARE
Make in terms of ()^2 which you can do by adding numbers to both sides. Eventually it will look like this:
(2x - 1)^2 - 7 = 0
Add to both sides, take a square root and then solve.

Be sure to solve for zero and be aware of negatives when plugging in.

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What logarithmic equation has the same solution as x-4=2^3
Solution 1

What logarithmic equation has the same solution as x-4=2^3

Solution:

x-4=2³

x-4=2*2*2

x-4=8

TO solve for x, Let us add 4 on both sides

x-4+4=8+4

x+0=12

So, x=12

But, x=12 is not a logarithmic equation and there are no options

So, an equation like, x=㏒

As log has base 10,

So, x=㏒ =12

So, logarithmic equation like x=log has same solution as x-4=2³

Solution 2

is required lograthmic equation.

Step-by-step explanation:

Given: Given equation, x - 4 = 2³

To find: Logarithmic function whose solution is same as given equation.

First we find the solution of given Equation.

consider,

x - 4 = 2³

x - 4 = 8        ( ∵ 2³ = 2×2×2 = 8 )

x = 8 + 4       ( Transposing 4 to RHS )

x = 12

Now we find the logarithmic equation whose solution is also x = 12.

( There exist many such equations )

Lets say one of them is,

Now we find its solution to check if it is same or not.

(using lograthmic rule,)

⇒ 2 × ( x + 2 ) = 28  (using lograthmic rule, )

⇒ 2x + 4 = 28

⇒ 2x = 28 - 4     (transposing 4 to RHS)

⇒ 2x = 24          (transposing 2 to RHS)

⇒ x = 12

Therefore, is required lograthmic equation.

Question
Two lines, C and D, are represented by the equations given below: Line C: y = x + 14 Line D: y = 3x + 2 Which of the following shows the solution to the system of equations and explains why?
Solution 1

The solution for the given system of equations are (6, 20).

What is a linear system of equations?

A system of linear equations is a set of two or more equations involving two or more variables. All of the equations must be considered at once in order to find the solution, which is any pair of values that makes each equation true independently.

The given system of linear equations are y=x+14 -----(i) and y=3x+2 -----(ii).

From equation (i) and (ii), we get

x+14=3x+2

3x-x=14-2

2x=12

x=6

Substitute x=6 equation (i), we get

y=20

Therefore, the solution for the given system of equations are (6, 20).

#SPJ3

Solution 2

(6, 20), because both lines pass through this point

Step-by-step explanation:

We see that both equations are equal to y.  This means we can set the two equations equal to each other:

x+14 = 3x+2

Subtract x from each side:

x+14-x = 3x+2-x

14 = 2x+2

Subtract 2 from each side:

14-2 = 2x+2-2

12 = 2x

Divide both sides by 2:

12/2 = 2x/2

6 = x

Substitute this into the first equation:

y = x+14

y = 6+14

y = 20

This makes the solution (6, 20).

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Fernando poured water from one-pint bottles into a three-gallon bucket. How many pints of water could the bucket hold?
Solution 1
Solution 2
24

One gallon holds eight pints. 8 x 3 = 24

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