solve the equation by completing the square round to da nearest hundred if nessesary.
x^2 + 10x = 18
A -11.56, 1.56
B 11.56, 1.56
C -11.56, - 1.56 my answer
D 11.56, -1.56
solve the equation by completing the square
x^2 + 9x -14 = 0
A 10.35, 1.35 Meh answer
B 10.35, -1.35
C -10.35, -1.35
D -10.35, 1.35
It is choice A.
-11.56,1.56
Reiny none of that is even close to any of the options for an answer
Well, well, well. Looks like you're in the mood for some equation-solving fun! Let's get clownin'!
For the first equation, x^2 + 10x = 18, we'll complete the square to find the solutions. As a funny side note, "completing the square" sounds like something a jigsaw puzzle enthusiast would say!
So, to complete the square, we take half the coefficient of x, square it, and add it to both sides of the equation. The coefficient of x is 10, half of which is 5. Squaring 5 gives us 25. Adding 25 to both sides:
x^2 + 10x + 25 = 43
Now we have a perfect square trinomial! The left side can be factored as (x + 5)^2, and our equation becomes:
(x + 5)^2 = 43
Next, we take the square root of both sides, being careful to include both positive and negative solutions:
x + 5 = ±√43
Subtracting 5 from both sides gives us the solutions:
x = -5 ± √43
Now, let's round those solutions to the nearest hundred:
The correct answer is either A (-11.56, 1.56) or C (-11.56, -1.56). So, choose your clown destiny!
Moving on to the second equation, x^2 + 9x - 14 = 0. It's time to complete the square again!
First, we need to rearrange the equation to have the x^2 and x terms together:
x^2 + 9x = 14
To complete the square, we take half the coefficient of x, which is 9 divided by 2, giving us 4.5. Squaring 4.5 gives us 20.25. Adding 20.25 to both sides:
x^2 + 9x + 20.25 = 34.25
Now we have another perfect square trinomial! The left side can be factored as (x + 4.5)^2, and our equation becomes:
(x + 4.5)^2 = 34.25
Next, taking the square root of both sides, again including both positive and negative solutions:
x + 4.5 = ±√34.25
Subtracting 4.5 from both sides:
x = -4.5 ± √34.25
Rounding those solutions to the nearest hundred, the correct answer is B (10.35, -1.35).
Now I hope those answers bring a smile to your face, or at least make you chuckle a little. Remember, math can be serious, but it doesn't have to be a circus!
To solve the equation x^2 + 10x = 18 by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation:
x^2 + 10x - 18 = 0
Step 2: Take half of the coefficient of x (which is 5) and square it:
(5)^2 = 25
Step 3: Add the square from Step 2 to both sides of the equation:
x^2 + 10x + 25 - 18 = 25
x^2 + 10x + 7 = 25
Step 4: Write the left side of the equation as a perfect square trinomial:
(x + 5)^2 = 25
Step 5: Take the square root of both sides of the equation, considering both positive and negative square roots:
x + 5 = ±√25
x + 5 = ±5
Step 6: Solve for x:
Case 1: x + 5 = 5
x = 5 - 5
x = 0
Case 2: x + 5 = -5
x = -5 - 5
x = -10
So the solutions for the equation x^2 + 10x = 18 are x = 0 and x = -10.
Now let's solve the equation x^2 + 9x - 14 = 0 by completing the square:
Step 1: Move the constant term to the other side of the equation:
x^2 + 9x = 14
Step 2: Take half of the coefficient of x (which is 4.5) and square it:
(4.5)^2 = 20.25
Step 3: Add the square from Step 2 to both sides of the equation:
x^2 + 9x + 20.25 = 14 + 20.25
x^2 + 9x + 20.25 = 34.25
Step 4: Write the left side of the equation as a perfect square trinomial:
(x + 4.5)^2 = 34.25
Step 5: Take the square root of both sides of the equation, considering both positive and negative square roots:
x + 4.5 = ±√34.25
Step 6: Solve for x:
Case 1: x + 4.5 = √34.25
x = √34.25 - 4.5
Case 2: x + 4.5 = -√34.25
x = -√34.25 - 4.5
Calculating the square root of 34.25, we find it is approximately 5.84.
So the solutions for the equation x^2 + 9x - 14 = 0 are approximately x = 5.84 - 4.5 = 1.34 (rounded to the nearest hundredth) and x = -5.84 - 4.5 = -10.34 (rounded to the nearest hundredth).
Therefore, the answer is option B: 10.35, -1.35.
follow these steps
1. If the x^2 term has a coefficient other than 1, divide each term by that coefficient.
(in both of your cases, we can skip that step)
2. take half of the coefficient of the x term
3.square that
4. Add this to both sides of the equation.
5. Your left side is now a perfect square, write it as such
6. Take the √ of both sides , make sure you have ± of the constant
7. isolate x and you are done
the first one:
1. x^2 + 10x = 18
2 ..... 1/2 of 10 is 5
3. 5^2 = 25
4. x^2 + 10x + 25 = 18 + 25
5. (x+5)^2 = 43
6. x+5 = ± √43
7. x = -5 ± √43
In a solution I would write:
x^2 + 10x = 18
x^2 + 10x + 25 = 18 + 25
(x+5)^2 = 43
x+5 = ±√43
x = -5 ± √43
you do the 2nd one in the same way, show me the steps