What is the solution of n² - 49 = 0
-7
7
±7
No Solution
What is the value of z so that -9 and 9 are both solutions of x² + z = 103
-22
3
22
184
n^2 = 49
well, 7^2 = 49
also (-7)^2 = (-7)(-7) = 49
well, 9^2 = (-9)^2 = 81
so, that means you need
81+z = 103
so, what do you think?
good choice.
To find the solutions to the equation n² - 49 = 0, you can use the concept of solving quadratic equations.
1. Start with the equation n² - 49 = 0.
2. Add 49 to both sides of the equation to isolate the quadratic term: n² = 49.
3. Take the square root of both sides of the equation to solve for n: n = ±√49.
4. Simplify the square root: n = ±7.
Therefore, the solutions to the equation n² - 49 = 0 are ±7.
Now let's find the value of z in the equation x² + z = 103, where -9 and 9 are both solutions.
1. Start with the equation x² + z = 103.
2. Plug in the first solution -9 for x: (-9)² + z = 103.
3. Simplify the quadratic term: 81 + z = 103.
4. Isolate z by subtracting 81 from both sides of the equation: z = 103 - 81.
5. Simplify: z = 22.
Now, repeat the above steps using the second solution 9 for x:
1. Start with the equation x² + z = 103.
2. Plug in the second solution 9 for x: (9)² + z = 103.
3. Simplify the quadratic term: 81 + z = 103.
4. Isolate z by subtracting 81 from both sides of the equation: z = 103 - 81.
5. Simplify: z = 22.
Therefore, the value of z that satisfies both -9 and 9 as solutions in the equation x² + z = 103 is 22.