All categories

2 years ago

Solve x^(2)+4x=4 for x by completing the square.

Mathematics

1 answer:

Mama L [17]2 years ago

8 0

Answer:

x = 2 sqrt(2) - 2 or x = -2 - 2 sqrt(2)

Step-by-step explanation:

Solve for x:

x^2 + 4 x = 4

Add 4 to both sides:

x^2 + 4 x + 4 = 8

Write the left hand side as a square:

(x + 2)^2 = 8

Take the square root of both sides:

x + 2 = 2 sqrt(2) or x + 2 = -2 sqrt(2)

Subtract 2 from both sides:

x = 2 sqrt(2) - 2 or x + 2 = -2 sqrt(2)

Subtract 2 from both sides:

Answer: x = 2 sqrt(2) - 2 or x = -2 - 2 sqrt(2)

You might be interested in

At Katya’s fruit stand, a basket of strawberries costs $4 and a basket of raspberries costs $9. In one morning, Katya sells 96 b

Tcecarenko [31]

Answer:

The number of strawberry baskets sold was 44

Step-by-step explanation:

Let

x ----> the number of strawberry baskets sold

y ---> the number of raspberries baskets sold

we know that

In one morning, Katya sells 96 baskets for $644

$x+y=96$ ----> equation A

$4x+9y=644$ ---> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (44.52)

see the attached figure

therefore

The number of strawberry baskets sold was 44 and the number of raspberries baskets sold was 52

4 0

3 years ago

Which expression is equivalent to x³ - x² - 14x + 24?

serg [7]

Answer:

<h3>Step-by-step explanation:</h3>

<h3>1. Use the rational root theorem</h3>

$= (x - 2) \frac{x ^{3} -x^{2} - 14x + 24}{x - 2}$

= ( x - 2 )( x² + x - 12 )

<h3>3. Factor x² + x - 12 : ( x -3 )( x + 4)</h3>

= ( x - 2 )( x - 3 )(x + 4 )

<h3>Solution : </h3>

3 0

1 year ago

Find the sum of 2x2 3x - 4, 8 - 3x, and -5x2 2. -3x2 - 2 -7x2 - 2 -3x2 6 -7x2 - 6x - 2

Law Incorporation [45]

-3x to the second power - 2

I believe this is your answer.

4 0

3 years ago

Hello help me with this question thanks in advance

Ede4ka [16]

$\bold{\huge{\green{\underline{ Solutions }}}}$

<h3>Answer 11 :-</h3>

We have, 

$\sf{HM = 5 cm }$

In square all sides of squares are equal

The perimeter of square 

$\sf{ = 4 × side }$

$\sf{ = 4 × 5 }$

$\sf{ = 20 cm }$

Thus, The perimeter of square is 20 cm

Hence, Option C is correct .

<h3>Answer 12 :-</h3>

We have, 

$\sf{MX = 3.5 cm }$

In square, diagonals are equal and bisect each other at 90°

Here, 

$\sf{MX = MT/2}$

$\sf{MT = 2 * 3.5 }$

$\sf{MT = 7 cm}$

Thus, The MT is 7cm long

Hence, Option C is correct .

<h3>Answer 13 :- </h3>

We have to find the measure of Angle MAT

All angles of square are 90° each

From above

$\sf{\angle{MAT = 90° }}$

Thus, Angle MAT is 90°

Hence, Option B is correct .

<h3>Answer 14 :-</h3>

We know that, 

All the angles of square are equal and 90° each

Therefore, 

$\sf{\angle{MHA = }}{\sf{\angle{ MHT/2}}}$

$\sf{\angle{MHA = 90°/2}}$

$\sf{\angle {MHA = 45°}}$

Thus, Angle MHA is 45°

Hence, Option A is correct

<h3>Answer 15 :- </h3>

Refer the above attachment for solution

Hence, Option A is correct

<h3>Answer 16 :- </h3>

Both a and b

The median of isosceles trapezoid is parallel to the base
The diagonals are congruent

Hence, Option C is correct

<h3>Answer 17 :-</h3>

In rhombus PALM,

All sides and opposite angles are equal

Let O be the midpoint of Rhombus PALM

In ΔOLM, By using Angle sum property :-

$\sf{35° + 90° + }{\sf{\angle{ OLM = 180°}}}$

$\sf{\angle{OLM = 180° - 125°}}$

$\sf{\angle{ OLM = 55° }}$

Now, 

$\sf{\angle{OLM = }}{\sf{\angle{OLA}}}$

OL is the bisector of diagonal AM

Therefore, 

$\sf{\angle{ PLA = 55° }}$

Thus, Angle PLA is 55° .

Hence, Option C is correct

8 0

2 years ago

The points H, I, J and K all lie on the same line segment, in that order, such that the

tresset_1 [31]

Answer:

IJ = 12

Step-by-step explanation:

sum the parts of the ratios, 3 + 3 + 4 = 10 parts

Divide HK by 10 to find the value of one part of the ratio.

40 ÷ 10 = 4 ← value of 1 part of ratio , then

IJ = 3 parts = 3 × 4 = 12

6 0

3 years ago