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beks73 [17]
3 years ago
11

Solve x2 + 14x = −24 by completing the square.

Mathematics
2 answers:
Artyom0805 [142]3 years ago
7 0

Answer:

A. -12, -2

Step-by-step explanation:

Just took an Edge quiz.

Aleks04 [339]3 years ago
6 0

Option A

The solution set of the equation is {-12, -2}

<h3><u>Solution:</u></h3>

Given equation is:

x^2 + 14x = -24

We have to find the solution set of this equation by completing the square

First, rearrange the equation so that only zero will be on the right side:

x^2 + 14x + 24 = 0 ----- eqn 1

<em><u>The general form of quadratic equation is:</u></em>

ax^2 + bx + c = 0 where a \neq 0

On comparing the given eqn 1 with general quadratic equation, we get

a = 1

b = 14

c = 24

In completing the square, we take half of coefficient of middle term "x" and then square it. Then we add it on both sides of the equation

So to complete the square, add (\frac{b}{2})^2 to both sides of the equation

x^2 + 14x + 24 + (\frac{14}{2})^2 = (\frac{14}{2})^2

x^2 + 14x + 24 + 7^2 = 7^2\\\\x^2 + 14x + 24 + 49 = 49

x^2 + 14x + 24 + 49 = 49\\\\x^2 + 14x + 49 = 49 - 24\\\\x^2 + 14x + 49 = 25\\\\(x + 7)(x + 7) = 25\\\\(x + 7)^2 = 25

Take square root on both sides

x + 7 = \sqrt{25}

x+7=\pm 5

Now make two equations

x + 7 = + 5 and x + 7 = -5

x = +5 - 7 = -2

x = -2

And,

x + 7 = -5

x = -5 - 7 = -12

x = -12

Therefore, the solution set of the equation is {-12, -2} and option A is correct

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shepuryov [24]

Answer: 16/25 (sorry I'm not really sure bc I'm just  a middle schooler)

Step-by-Step explanation:

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3 3/4 minutes=3.75 minutes

2.4/3.75=240/375

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you can solve the problem using the fractions...

2 2/5=12/5

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(12/5)/(15/4)=(12/5)*(4/15)=48/75=16/25=0.64 again, or you can simplify before multiplying...

(12/5)/(15/4)=(12/5)*(4/15)=(4/5)*(4/5)=16/25...

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Kipish [7]

Answer:

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Step-by-step explanation:

Amy is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.95. See the figure below. Amy has 48 miles remaining after 31 minutes of driving. How many miles will be remaining after 47 minutes of driving?

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weqwewe [10]

Answer:

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