Solve The Quadratic Equation By Using Square Roots Worksheet

Algebra 2
Quadratic Equations

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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 xx.\newlinex2=25x^2 = 25\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______
Solution:
  1. Square Root of Equation: x2=25x^2 = 25 \newlineFind the values of xx.\newlineTake the square root of both sides of the equation.\newlinex=±25x = \pm\sqrt{25}
  2. Calculate Square Root: Calculate the square root of 2525.x=±5x = \pm 5
  3. Write Solutions: Write down the two possible solutions for xx.\newlineValues of xx: 55, 5-5
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About Worksheet

Algebra 2
Quadratic Equations

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.

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