How to Solve a Quadratic Equation? (+FREE Worksheet!)

Learn how to simplify and solve a Quadratic Equation in a few simple and easy steps.

How to Solve a Quadratic Equation? (+FREE Worksheet!)

Related Topics

Step by step guide to Solving a Quadratic Equation

  1. Write the equation in the form of: \(ax^2+bx+c=0\)
  2. Factorize the quadratic and solve for the variable.
  3. Use quadratic formula if you couldn’t factorize the quadratic.
  4. Quadratic formula: \( \color{blue}{x=\frac{-b±\sqrt{b^2-4ac}}{2a}}\)

Solving a Quadratic Equation – Example 1:

Find the solutions of each quadratic. \(x^2+7x+10=0\)

Answer:

\(x^2+7x+10=0\)

You can use factorization method. \(x^2+7x+10=0\)

\((x+5)(x+2)=0\)
Then: \((x=-5)\) and \((x=-2)\)
You can also use quadratic formula: \(=\frac{-b±\sqrt{b^2-4ac}}{2a} , a=1,b=7\) and \(c=10\), then: \(x=\frac{-7±\sqrt{7^2-(4)×(1)×(10)}}{2×1}\)
\(x_{1}=\frac{-7+\sqrt{7^2-(4) × (1) × (10)}}{2 × 1}= \frac{-7+\sqrt{49-40}}{2}= \frac{-7+\sqrt{9}}{2} = \frac{-7+3}{2} =\frac {-4}{2}= -2\) ,

\(x_{2}=\frac{-7-\sqrt{7^2-(4) × (1) × (10)}}{2 × 1}= \frac{-7-\sqrt{49-40}}{2}= \frac{-7-\sqrt{9}}{2} = \frac{-7-3}{2} =\frac {-10}{2}= -5\)

Solving a Quadratic Equation – Example 2:

Find the solutions of each quadratic. \(x^2+4x+3=0\)

Answer:

Use quadratic formula: \(=\frac{-b±\sqrt{b^2-4ac}}{2a} , a=1,b=4\) and \(c=3 \), then: \(x=\frac{-4±\sqrt{4^2-(4) × (1) × (3)}}{2 × 1}\)

\(x_{1}=\frac{-4+\sqrt{4^2-(4) × (1) × (3)}}{2 × 1}= \frac{-4+\sqrt{16-12}}{2}= \frac{-4+\sqrt{4}}{2} = \frac{-4+2}{2} =\frac {-2}{2}= -1\),

\(x_{2}=\frac{-4-\sqrt{4^2-(4) × (1) × (3)}}{2 × 1}= \frac{-4-\sqrt{16-12}}{2}= \frac{-4-\sqrt{4}}{2} = \frac{-4-2}{2} =\frac {-6}{2}= -3\)

Solving a Quadratic Equation – Example 3:

Find the solutions of each quadratic. \(x^2+5x-6\)

Answer:

Use quadratic formula: \(=\frac{-b±\sqrt{b^2-4ac}}{2a} , a=1,b=5\) and \(c=-6\) , then: \(x=\frac{-5±\sqrt{5^2-(4) × (1) × (-6)}}{2 × 1}\) ,

\(x_{1}=\frac{-5+\sqrt{5^2-(4) × (1) × (-6)}}{2 × 1}= \frac{-5+\sqrt{25+24}}{2}= \frac{-5+\sqrt{49}}{2} = \frac{-5+7}{2} =\frac {2}{2}= 1\),

\(x_{2}=\frac{-5-\sqrt{5^2-(4) × (1) × (-6)}}{2 × 1}= \frac{-5-\sqrt{25+24}}{2}= \frac{-5-\sqrt{49}}{2} = \frac{-5-7}{2} =\frac {-12}{2}= -6\)

Solving a Quadratic Equation – Example 4:

Find the solutions of each quadratic. \(x^2+6x+8\)

Answer:

Use quadratic formula: \(=\frac{-b±\sqrt{b^2-4ac}}{2a} , a=1,b=6\) and \(c=8\), then: \(x=\frac{-6±\sqrt{6^2-(4) × (1) × (8)}}{2 × 1}\) ,

\(x_{1}=\frac{-6+\sqrt{6^2-(4) × (1) × (8)}}{2 × 1}= \frac{-6+\sqrt{36-32}}{2}= \frac{-6+\sqrt{4}}{2} = \frac{-6+2}{2} =\frac {-4}{2}= -2\),

\(x_{2}=\frac{-6-\sqrt{6^2-(4) × (1) × (8)}}{2 × 1}= \frac{-6-\sqrt{36-32}}{2}= \frac{-6-\sqrt{4}}{2} = \frac{-6-2}{2} =\frac {-8}{2}= -4\)

Exercises for Solving a Quadratic Equation

Solve each equation.

  • \(\color{blue}{x^2-5x-14=0}\)
  • \(\color{blue}{x^2+8x+15=0}\)
  • \(\color{blue}{x^2-5x-36=0}\)
  • \(\color{blue}{x^2-12x+35=0}\)
  • \(\color{blue}{x^2+12x+32=0}\)
  • \(\color{blue}{5x^2+27x+28=0}\)

Download Solving a Quadratic Equation Worksheet

  • \(\color{blue}{x=-2,x=7}\)
  • \(\color{blue}{x=-3,x=-5}\)
  • \(\color{blue}{x=9,x=-4}\)
  • \(\color{blue}{x=7,x=5}\)
  • \(\color{blue}{x=-4,x=-8}\)
  • \(\color{blue}{x=-\frac{7}{5},x=-4}\)

Related to "How to Solve a Quadratic Equation? (+FREE Worksheet!)"

How to Determine Limits Using the Squeeze Theorem?How to Determine Limits Using the Squeeze Theorem?
How to Determine Limits Using Algebraic Manipulation?How to Determine Limits Using Algebraic Manipulation?
How to Estimate Limit Values from the Graph?How to Estimate Limit Values from the Graph?
Properties of LimitsProperties of Limits
How to Find the Expected Value of a Random Variable?How to Find the Expected Value of a Random Variable?
How to Define Limits Analytically Using Correct Notation?How to Define Limits Analytically Using Correct Notation?
How to Solve Multiplication Rule for Probabilities?How to Solve Multiplication Rule for Probabilities?
How to Solve Venn Diagrams and the Addition Rule?How to Solve Venn Diagrams and the Addition Rule?
How to Find the Direction of Vectors?How to Find the Direction of Vectors?
Vectors IntroductionVectors Introduction

What people say about "How to Solve a Quadratic Equation? (+FREE Worksheet!)"?

  1. I believe there’s a typo in the x²+5x-6 example –>>
    -5 -√4²-4•1(-6)
    where it should be
    -5 -√5²-4•1(-6)

    I may be stupid though..

    • You are definitely right! Thank you for letting us know.
      It’s revised now.

Leave a Reply