Math / Algebra

QuestionWhat are the solutions to $100 x^{2}-1=0$ ? Use the keypad to enter your answers in the boxes. Find more symbols by using the drop-down arrow at the top of the keypad.
The solutions to the quadratic equation are $x=$ $\square$ and $x=$ $\square$

Studdy Solution

STEP 1

What is this asking? We need to find the values of $x$ that make the equation $100x^2 - 1 = 0$ true.
It's like a puzzle where $x$ is the missing piece! Watch out! There are two solutions to this kind of equation, so don't forget to find both!
Also, be careful with the signs – positive and negative matter a lot!

STEP 2

1. Isolate the $x^2$ term
2. Take the square root of both sides
3. Find the two solutions

STEP 3

We start with $100x^2 - 1 = 0$ .
To get $x^2$ by itself, we need to move that $-1$ to the other side.
We can do that by adding $1$ to both sides of the equation.
Remember, what we do to one side, we must do to the other to keep things balanced!
This gives us: $100x^2 - 1 + 1 = 0 + 1$ $100x^2 = 1$

STEP 4

Now, that $100$ is stuck to the $x^2$ .
Let's divide both sides by 100 to get $x^2$ all alone: $\frac{100x^2}{100} = \frac{1}{100}$ $x^2 = \frac{1}{100}$ Awesome! We've isolated $x^2$ !

STEP 5

To get $x$ by itself, we need to undo that square.
We can do that by taking the square root of both sides: $\sqrt{x^2} = \sqrt{\frac{1}{100}}$ Remember, whenever we take the square root, we get two possible answers: a positive one and a negative one!

STEP 6

We can simplify the right side because the square root of a fraction is the same as the square root of the top divided by the square root of the bottom: $x = \pm \frac{\sqrt{1}}{\sqrt{100}}$ Since $\sqrt{1} = 1$ and $\sqrt{100} = 10$ , we get: $x = \pm \frac{1}{10}$

STEP 7

The plus-or-minus symbol ( $\pm$ ) means we have two solutions: $x = \frac{1}{10}$ and $x = -\frac{1}{10}$

STEP 8

The solutions are $x = \frac{1}{10}$ and $x = -\frac{1}{10}$ .

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QuestionWhat are the solutions to $100 x^{2}-1=0$ ? Use the keypad to enter your answers in the boxes. Find more symbols by using the drop-down arrow at the top of the keypad.
The solutions to the quadratic equation are $x=$ $\square$ and $x=$ $\square$

Studdy Solution

STEP 1

STEP 2

1. Isolate the $x^2$ term
2. Take the square root of both sides
3. Find the two solutions

STEP 3

We start with $100x^2 - 1 = 0$ .
To get $x^2$ by itself, we need to move that $-1$ to the other side.
We can do that by adding $1$ to both sides of the equation.
Remember, what we do to one side, we must do to the other to keep things balanced!
This gives us: $100x^2 - 1 + 1 = 0 + 1$ $100x^2 = 1$

STEP 4

Now, that $100$ is stuck to the $x^2$ .
Let's divide both sides by 100 to get $x^2$ all alone: $\frac{100x^2}{100} = \frac{1}{100}$ $x^2 = \frac{1}{100}$ Awesome! We've isolated $x^2$ !

STEP 5

To get $x$ by itself, we need to undo that square.
We can do that by taking the square root of both sides: $\sqrt{x^2} = \sqrt{\frac{1}{100}}$ Remember, whenever we take the square root, we get two possible answers: a positive one and a negative one!

STEP 6

We can simplify the right side because the square root of a fraction is the same as the square root of the top divided by the square root of the bottom: $x = \pm \frac{\sqrt{1}}{\sqrt{100}}$ Since $\sqrt{1} = 1$ and $\sqrt{100} = 10$ , we get: $x = \pm \frac{1}{10}$

STEP 7

The plus-or-minus symbol ( $\pm$ ) means we have two solutions: $x = \frac{1}{10}$ and $x = -\frac{1}{10}$

STEP 8

The solutions are $x = \frac{1}{10}$ and $x = -\frac{1}{10}$ .

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QuestionWhat are the solutions to 100x2−1=0100 x^{2}-1=0100x2−1=0 ? Use the keypad to enter your answers in the boxes. Find more symbols by using the drop-down arrow at the top of the keypad.The solutions to the quadratic equation are x=x=x= □\square□ and x=x=x= □\square□

Studdy Solution

STEP 1

STEP 2

1. Isolate the x2x^2x2 term2. Take the square root of both sides3. Find the two solutions

STEP 3

STEP 4

Now, that 100100100 is stuck to the x2x^2x2.Let's *divide* both sides by **100** to get x2x^2x2 all alone: 100x2100=1100 \frac{100x^2}{100} = \frac{1}{100} 100100x2​=1001​ x2=1100 x^2 = \frac{1}{100} x2=1001​Awesome! We've isolated x2x^2x2!

STEP 5

To get xxx by itself, we need to undo that square.We can do that by taking the **square root** of both sides: x2=1100 \sqrt{x^2} = \sqrt{\frac{1}{100}} x2​=1001​​ Remember, whenever we take the square root, we get *two* possible answers: a positive one and a negative one!

STEP 6

STEP 7

The plus-or-minus symbol (±\pm±) means we have *two* solutions: x=110 x = \frac{1}{10} x=101​ and x=−110 x = -\frac{1}{10} x=−101​

STEP 8

The solutions are x=110x = \frac{1}{10}x=101​ and x=−110x = -\frac{1}{10}x=−101​.

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionWhat are the solutions to $100 x^{2}-1=0$ ? Use the keypad to enter your answers in the boxes. Find more symbols by using the drop-down arrow at the top of the keypad.
The solutions to the quadratic equation are $x=$ $\square$ and $x=$ $\square$

1. Isolate the $x^2$ term
2. Take the square root of both sides
3. Find the two solutions

Now, that $100$ is stuck to the $x^2$ .
Let's divide both sides by 100 to get $x^2$ all alone: $\frac{100x^2}{100} = \frac{1}{100}$ $x^2 = \frac{1}{100}$ Awesome! We've isolated $x^2$ !

To get $x$ by itself, we need to undo that square.
We can do that by taking the square root of both sides: $\sqrt{x^2} = \sqrt{\frac{1}{100}}$ Remember, whenever we take the square root, we get two possible answers: a positive one and a negative one!

The plus-or-minus symbol ( $\pm$ ) means we have two solutions: $x = \frac{1}{10}$ and $x = -\frac{1}{10}$

The solutions are $x = \frac{1}{10}$ and $x = -\frac{1}{10}$ .