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3 years ago

Solve x2 - 4x - 7 = 0 by completing the square. What are the solutions?

Mathematics

1 answer:

Roman55 [17]3 years ago

5 0

Answer:

x= 2 + √11 or x = 2 −√11

Step-by-step explanation:

I am going to complete the square step-by-step.

x² − 4x − 7=0

Step 1: Add 7 to both sides.

x² − 4x − 7+ 7 = 0 + 7

x² − 4x = 7

Step 2: The coefficient of -4x is -4. Let b = -4.

Then we need to add (b/2)² = 4 to both sides to complete the square.

Add 4 to both sides.

x² − 4x + 4 = 7 + 4

x² − 4x + 4 = 11

Step 3: Factor left side.

(x−2)² = 11

Step 4: Take square root.

x − 2 = ±√11

Step 5: Add 2 to both sides.

x − 2 + 2 = 2 ±√11

x = 2 ±√11

x= 2 + √11 or x = 2 −√11

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Round 40.32 to the nearest whole number?

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3 years ago

Read 2 more answers

Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.

mariarad [96]

The height of the triangle is approximately $4.35\text{ mm}$

Step-by-step explanation:

The area of a triangle can be calculated by using the Heron's formula.

Heron's formula: 

Suppose a triangle has sides $a'$ , $b'$ and $c'$ , then the semi-perimeter $S$ of the triangle is represented by the expression,

$S=\frac{a'+b'+c'}{2}$

The area $A$ of the traingle is formulated below.

$\fbox {\begin\\A=\sqrt{s(s-a')(s-b')(s-c')}\end{minispace}}$

To calculate the area of the triangle with sides $9 \text{ mm}$ , $6 \text{ mm}$ and $12 \text{ mm}$ , first find the semi-perimeter.

$S=\frac{9+6+12}{2}\\S=\frac{27}{2}\\S=13.5 \text{ mm}$

Now, the area of the triangle is calculated below.

$A=\sqrt{s(s-a)(s-b)(s-c)}\\A=\sqrt{13.5(13.5-9)(13.5-6)(13.5-12)}\\A=\sqrt{13.5 \times 4.5 \times 7.5 \times 1.5}\\A=\sqrt{\frac{135}{10}\times\frac{45}{10}\times\frac{75}{10}\times\frac{15}{10}} \\A=\sqrt{\frac{(15\times3\times3) \times (15\times3) \times (15\times5) \times15}{100\times100}}\\A=\frac{15\times15\times3\sqrt{15 } }{100} \\A=2.25\times3\times3.87\\A=26.122$

Area A of a triangle with a altitude P and one side as base B on which the altitude P is drawn, can be calculated as,

$\fbox{\begin\\A= \left[\frac{1}{2}(B)(P)\right]\\\end{minispace}}$

Now, the area of the same triangle can also be calculated as,

$A=\frac{1}{2}(12)(x)\\A=6x$

In the above calculations, area of the triangle is calculated in two ways.

Therefore, both the areas can be equated to obtain the altitude $x$ .

$6x=26.122\\x=\frac{26.122}{6}\\x=4.35$

Thus, the height of the triangle is evaluated as $\fbox{4.35 \text{ mm}}$ .

Learn more:

1. Prove that AB2+BC2=AC2https://brainly.com/question/1591768

2. Which undefined term is needed to define an angle? brainly.com/question/3717797

3. Look at the figure, which trigonometric ratio should you use to find x? brainly.com/question/9880052

Answer Details

Grade: Junior High School

Subject: Mathematics

Chapter: Area of triangle

Keywords: area of triangle, heron's formula, base multiplied by height, base multiplied by perpendicular, base multiplied by altitude, right triangle, altitude corresponding to base, area of right triangle

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3 years ago

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OLEGan [10]

Answer:

Step-by-step explanation:

Please kindly check the attached

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4 years ago

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