Completing the square: Which of the following is a solution x^2 + 14x + 112 = 0? If necessary round to the nearest hundredth.

Question

Create an image that visually represents a mathematical problem involving the concept of 'completing the square'. The image should include the representation of quadratic equation x^2 + 14x + 112 = 0 on a 2D graph. There should be visible indications of potential solutions, including -0.24, -4.24, 4.24, and no solution somewhere on the plot, using symbols such as markers or points, but not text. Also, depict the solutions x= 0.9 and x=-14.9 as distinct symbols differently from the other solutions, indicating a point of confusion or error.

Completing the square: Which of the following is a solution x^2 + 14x + 112 = 0? If necessary round to the nearest hundredth.

x= -0.24
x= -4.24
x= 4.24
no solution

I worked it and got neither of the answers. I got x= 0.9 and x=-14.9. Where did I go wrong? Thanks

Answer 1

1.C. 30.25

2.B. -1
3.D. no solution
4.B. 8 in
Connexus academy algebra 1

Answer 2

Yes they are both correct

Answer 3

Apple still correct

Answer 4

Need to factor end terms so the factors will sum to the middle term. I see no solution.

112 = 2 * 2 * 2 * 2 * 7

I don't know how you got your answers, since .9 * 14.9 = 13.1. Also x would not be positive, since the end term is positive. It would have to be (x+?)(x+?) = 0. That would lead both values of x to be negative.

Do you have typos in your post?

Answer 5

mine had mixed up answeres so i just matched whichever answer was on each slide to the one apple posted and i got 100

Answer 6

To find the solutions to the equation x^2 + 14x + 112 = 0 using completing the square, you can follow these steps:

1. Move the constant term (112) to the other side of the equation:
x^2 + 14x = -112

2. To complete the square, divide the coefficient of x (14) by 2, and then square it:
(14/2)^2 = 49

3. Add the result from step 2 to both sides of the equation:
x^2 + 14x + 49 = -112 + 49
x^2 + 14x + 49 = -63

4. Factor the left side of the equation:
(x + 7)^2 = -63

5. Take the square root of both sides of the equation:
√[(x + 7)^2] = ±√(-63)

6. Simplify the square root of the negative number by using the imaginary unit (i):
(x + 7) = ±√(63)i

7. Subtract 7 from both sides of the equation:
x = -7 ± √(63)i

So, the solutions to x^2 + 14x + 112 = 0 are x = -7 + √(63)i and x = -7 - √(63)i. These solutions involve the imaginary unit (i), indicating that there are no real solutions to the equation.

It appears that there was an error in your calculations, leading to different solutions. Double-check your work in completing the square, and ensure that you correctly square and simplify the expressions.