# Solve The Quadratic Equation By Using Square Roots Worksheet

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To solve a quadratic equation like $$ax^2 + bx + c = 0$$ using square roots, first identify $$a$$, $$b$$, and $$c$$. Divide the equation by $$a$$ to simplify. Rearrange to isolate $$x^2$$. Take the square root of both sides to find two solutions for $$x$$: one positive and one negative. This method helps determine where the equation intersects the x-axis on a graph.

Algebra 2

## How Will This Worksheet on “Solve the Quadratic Equation by Using Square Roots” Benefit Your Student's Learning?

• Reinforces understanding of quadratic equations and their solutions.
• Develops critical thinking and problem-solving skills.
• Improves algebraic manipulation and equation-solving abilities.
• Enhances graphical interpretation of quadratic functions.
• Applies math concepts to real-world scenarios.
• Builds foundational knowledge for advanced math topics.
• Fosters self-directed learning and confidence.
• Prepares for assessments and standardized tests.

## How to Solve the Quadratic Equation by Using Square Roots?

• Ensure the quadratic equation is in the standard form $$ax^2 + bx + c = 0$$, where $$a$$, $$b$$, and $$c$$ are constants.
• Identify the values of $$a$$, $$b$$, and $$c$$.
• Divide the equation by $$a$$ to make the coefficient of $$x^2$$ equal to 1.
• Move $$x^2$$ to one side and everything else to the other.
• Take the square root of both sides.
• Solve for $$x$$ using both the positive and negative square roots.
• Simplify the solutions if necessary.

## Solved Example

Q. Solve for $x$.$\newline$$x^2 = 25$$\newline$Write your answer in simplified, rationalized form.$\newline$$x =$ ______ or $x =$ ______
Solution:
1. Square Root of Equation: $x^2 = 25$ $\newline$Find the values of $x$.$\newline$Take the square root of both sides of the equation.$\newline$$x = \pm\sqrt{25}$
2. Calculate Square Root: Calculate the square root of $25$.$x = \pm 5$
3. Write Solutions: Write down the two possible solutions for $x$.$\newline$Values of $x$: $5$, $-5$

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