Step-By-Step-Math: Solving Quadratic Equations Using the Quadratic Formula
Solve 2x² + 5x − 3 = 0 Using the Quadratic Formula | Step by Step
Learning Target: I can solve quadratic equations using the quadratic formula
What You'll Learn
- Identify coefficients a, b, and c
- Apply the quadratic formula correctly
- Interpret and simplify exact solutions
Key Terms
quadratic equation, quadratic formula, discriminant, coefficient, solution, radical
Standards Alignment
- CCSS.MATH.CONTENT.HSA.REI.B.4: Solve quadratic equations in one variable
- CCSS.MATH.CONTENT.HSA.REI.B.4.A: Use the quadratic formula to solve quadratic equations
Math Practices
- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP6: Attend to precision
Chapters
- 0:00 How do you solve 2x² + 5x − 3 = 0?
- 0:12 What is the standard form of a quadratic equation?
- 0:18 How do you identify coefficients a, b, and c?
- 0:27 What is the quadratic formula?
- 0:39 How do you substitute values into the quadratic formula?
- 0:51 How do you simplify under the radical?
- 1:00 What is the first solution using the plus case?
- 1:07 What is the second solution using the minus case?
- 1:15 What are the final solutions to 2x² + 5x − 3 = 0?
- 1:25 How do you verify the solutions by factoring?
- 2:05 Final2
- 2:22 Questions
- 2:44 Signoff
▶ Click to Read Full Transcript
[00:00] Let's solve this quadratic equation step by step. Our instructions are to solve for x, given the quadratic equation 2 x squared plus 5 x minus 3 equals 0.
[00:12] Quadratic equations come in the form, a x squared plus b x plus c equals 0.
[00:18] First, identify the coefficients. a equals 2, b equals 5, and c equals negative 3.
[00:27] Now substitute these into the quadratic formula. The quadratic formula is, x equals negative b, plus or minus the square root of b squared minus 4 a c, all over 2 a.
[00:41] Substituting our values, we get x equals negative 5, plus or minus the square root of 5 squared, or 5 times 5, minus 4 times 2 times negative 3 all over 4.
[00:54] Simplifying, 5 squared is 25, and 4 times 2 times negative 3 is negative 24. We are subtracting negative 24, so minus negative 24 is plus positive 24. After simplifying, we get x equals negative 5, plus or minus the square root of 25 plus 24, all over 4.
[01:17] Simplify under the radical. 25 plus 24 is 49. The square root of 49 is 7. We use both plus and minus because a square root can be positive or negative, so we have two solutions.
[01:32] For the plus case: negative 5 plus 7 is 2, divided by 4, gives us one half. Our first solution is x equals one half.
[01:43] For the minus case: negative 5 minus 7 is negative 12, divided by 4, gives us negative 3. Our second solution is x equals negative 3.
[01:55] So our two solutions are x equals one half, and x equals negative 3. We can verify this by writing the equation in factored form.
[02:05] Since x equals one half and x equals negative 3, this is the same as the quantity 2 x minus 1, times the quantity x plus 3, equals 0, which expands back to our original equation 2 x squared plus 5 x minus 3 equals 0.
[02:22] Questions about that last step? No worries. Notice that 2x minus 1 equals 0 gives x equals one half, and x plus 3 equals 0 gives x equals negative 3. That is how factoring and the quadratic formula connect. To learn more, search for multiplying polynomials and factoring.
[02:44] I hope you found this helpful along your journey to discovering the joy in mathematics. This has been Mister Marx AI. Until next time, keep up the good work!
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