How do you isolate $$x^2$$ in a quadratic equation?

To isolate $$x^2$$ , you need to move all other terms to the opposite side of the equation. For example, in $$x^2 - 1 = 39$$ , add 1 to both sides to get $$x^2 = 40$$ .

Solve the equation using Square Roots Method: $$x^2 - 1 = 39$$

$$x = -2\sqrt{10},\ 2\sqrt{10}$$ .

Solve the equation using Square Roots Method: $$5x^2 = 90$$

$$x = -3\sqrt{2},\ 3\sqrt{2}$$ .

What is the first step in solving $$x^2 - 100 = 0$$ using the Square Roots Method?

The first step is to isolate $$x^2$$ by adding 100 to both sides, resulting in $$x^2 = 100$$ .

Solve the equation using Square Roots Method: $$-3x^2 + 297 = 0$$

$$x = -3\sqrt{11},\ 3\sqrt{11}$$ .

Solve the equation using Square Roots Method: $$25x^2 = 4$$

$$x = -\frac{2}{5},\ \frac{2}{5}$$ .

What is the significance of the square root symbol in the Square Roots Method?

The square root symbol indicates that there are two possible solutions: one positive and one negative.

How do you check your solution after using the Square Roots Method?

Substitute the found values of $$x$$ back into the original equation to verify that both sides are equal.

What is the general form of a quadratic equation?

The general form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where $$a$$ , $$b$$ , and $$c$$ are constants.

What is the relationship between the coefficients and the roots of a quadratic equation?

The sum of the roots is equal to $$-\frac{b}{a}$$ and the product of the roots is equal to $$\frac{c}{a}$$ .

What is the purpose of the Square Roots Method?

The purpose of the Square Roots Method is to provide a straightforward way to solve quadratic equations that can be expressed in the form $$x^2 = k$$ .

What is the solution set for the equation $$x^2 = 0$$ ?

The solution set is $$x = 0$$ , which is a repeated root.

Solving Quadratics by Square Roots Method Flashcards

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1.

FLASHCARD QUESTION

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What is the Square Roots Method in solving quadratics?

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CCSS.HSA-REI.B.4B

2.

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CCSS.8.EE.A.2

3.

FLASHCARD QUESTION

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CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

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CCSS.HSA-REI.B.4B

5.

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CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

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CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

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What does it mean if a quadratic equation has no real solution?

Back

It means that the equation does not intersect the x-axis, often indicated by a negative value under the square root when using the Square Roots Method.

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CCSS.HSA-REI.B.4B

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