Solving math equation like 58: 2x^2 – 9x^2; 5 – 3x + y + 6 is an important skill. It can be tricky, but we will break it down step by step in this article. We will learn different ways to make the problem easier and find the values of ‘x’ and ‘y’ that make the equation true. By the end, you will feel more confident in solving equations like this one.
Also Read: X²-11x+28=0: Quadratic Equation
This equation has some numbers and letters in it. The numbers are 58, 2, 9, 5, 3, and 6. The letters are x and y. We need to do some math to figure out what the answer is.
Basic Information about Equation 58: 2x^2 – 9x^2; 5 – 3x + y + 6
Before we figure out the answer, let’s look at the equation more closely. The equation has three parts: 2x^2, -9x^2, and 5 – 3x + y + 6. Our main goal is to find the values of ‘x’ and ‘y’ that make the equation true.
Combining like terms
Combining like terms means putting together numbers or variables that are the same. It’s like when you have a pile of blue blocks and a pile of red blocks, and you put all the blue blocks together and all the red blocks together. It makes it easier to see how many blocks you have in total. In math, we do the same thing with numbers and variables to simplify and solve equations.
To make the equation easier, we put together the parts that are the same. In this case, we have two parts that have x^2, which are 2x^2 and -9x^2. When we put them together, we get -7x^2. The equation now looks like this: 58: -7x^2; 5 – 3x + y + 6.
Isolating Variables
Isolating ‘x’ means figuring out what the value of ‘x’ is by itself.
To keep going with finding the values of ‘x,’ we want to put ‘x’ all by itself on one side of the equation. We can do this by moving all the parts of the equation that have ‘x’ to one side, and the numbers that don’t have ‘x’ to the other side.
There is a math problem that says negative seven times a number squared is equal to fifty-eight minus the total of five and six, plus another number called y.
Separating the letter ‘y’ from the rest of the problem.
To find out what ‘y’ is, we have to move it to one side of the math problem.
This equation is like a puzzle that helps us figure out what number y is. We start with the number 58, then subtract the sum of 5 and 6, and then subtract 7 times the square of a number called x.
Using the Quadratic Formula
Using the Quadratic Formula is a way to solve math problems that involve numbers squared. It helps us find the values of the numbers that make the equation true.
Because of a term in the equation that looks like -7 times x squared, we can use a special formula to find the answers for ‘x’. This formula is called the quadratic formula. It says that for an equation with terms like ax squared, bx, and c, the answers for ‘x’ can be found using this formula.
This is a formula that helps us find the answer to a math problem with numbers a, b, and c. The answer will be two different numbers, one with a plus sign and one with a minus sign.
We have a math problem with three numbers, a, b, and c. In this problem, a is -7, b is 0, and c is equal to 58 minus the numbers 5 and 6 added together, plus another number called y. We can use a special formula called the quadratic formula to solve this problem. When we put these numbers into the formula, we can find the answer.
x = (-b ± √(b^2 – 4ac)) / 2a
In our equation, a = -7, b = 0, and c = 58 – (5 + 6) + y. Substituting these values into the quadratic formula, we get:
x = (± √(0 – 4*(-7)(58 – (5 + 6) + y))) / 2(-7)
Checking the solutions means making sure the answers are correct.
Once you find the numbers for ‘x’ using any method, it’s important to check if they are correct by putting them back into the original question. This helps make sure that both sides of the question are the same and that your answers are right.
Graphical representation
A graphical representation is a way of showing information or data using pictures or images instead of just words or numbers. It can help us understand things better by making them easier to see and understand. For example, instead of reading a long list of numbers, we can use a graph to show how those numbers relate to each other and how they change over time.
Another way to understand the solutions is by drawing a picture on a graph. We can see where the line crosses the x-axis to find the answers for ‘x.’ The picture also helps us learn more about how the equation works.
conclusion
The conclusion is like the ending or final part of a story. It’s where everything comes together and we learn the main idea or lesson.
Solving equations is a really important skill that helps us in lots of different areas of math and other subjects. In this article, we figured out how to solve a tricky equation using different ways, like separating the letters and using a special math formula. By learning these methods, you can feel confident about solving other equations too and getting the right answers.