Today, we’ll explore a cool math quadratic equation. It’s a fun math problem, (x2 – 11x + 28 = 0) for which we’ll find the answer to the value of ‘x’. Don’t worry if big numbers make you go, “Howw?” We’ll take it step by step, just like putting together a jigsaw puzzle.
Ready to crack the code with us? Let’s jump right in. And don’t worry, we’ll break it down into simple, easy-to-follow steps.
Step 1: Recognize the type of Equation
Our equation (x2 – 11x + 28 = 0) is quadratic because it has an (x^2) term.
Quadratic equations look like (ax2 + bx + c = 0), where (a), (b), and (c) are numbers.
Step 2: Factor the Expression
We’re going to factor the expression (x2 – 11x + 28). Here’s how:
-> Find two numbers that multiply to (28) and add up to (-11). These numbers are (-4) and (-7).
-> Rewrite the expression as (x – 4)(x – 7)
Recommended Reading: Algebraic Expressions
Step 3: Apply the Zero-Product Property
The Zero-Product Property says if we have two things multiplying to give (0), then at least one of them must be (0). So, we set each factor equal to (0) and solve for (x).
Step 4: Solve for (x)
Let’s set (x – 4 = 0) and (x – 7 = 0) and solve for (x):
-> (x – 4 = 0) gives (x = 4).
-> (x – 7 = 0) gives (x = 7).
Step 5: Verify Solutions
We check if (x = 4) and (x = 7) work in the original equation (x2 – 11x + 28 = 0).
When (x = 4):
-> (42 – 11(4) + 28 = 0) simplifies to (0 = 0), which is true.
When (x = 7):
-> (72 – 11(7) + 28 = 0) simplifies to (0 = 0), which is also true.
Recommended Reading: Solving x^x^x =2 using Infinite Exponent Tower Trick
Conclusion
By following these simple steps, we found that the solutions to (x2 – 11x + 28 = 0) are (x = 4) and (x = 7). Factoring is a handy method for solving quadratic equations. Keep practicing, and you’ll master it in no time. If you have any more questions, feel free to ask.
We hope this article has been helpful. If you have any questions, please feel free to comment below.
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