X²-9=0
X²+7=0
3x²=0
1/4x²-4=0
64b²=16
144-p²=0
5z²-45=0
H²=-49
5²-35=-35
Solution:
X²-9=0 can be factored as (x+3)(x-3)=0. Therefore, x can be either 3 or -3.
X²+7=0 cannot be factored further using real numbers. Therefore, the solution is not a real number.
3x²=0 can be simplified to x²=0, which means x=0.
1/4x²-4=0 can be simplified to 1/4x²=4 or x²=16. The solutions are x=4 and x=-4.
64b²=16 can be simplified to 8b=±2 or b=±1/4.
144-p²=0 can be simplified to (12+p)(12-p)=0. Therefore, p can be either 12 or -12.
5z²-45=0 can be simplified to 5z²=45, which means z²=9. The solutions are z=3 and z=-3.
H²=-49 can be simplified to H=±7i, where i is the imaginary unit.
5²-35=-35 is not a valid equation.
To solve these equations step-by-step:
1) X² - 9 = 0
Add 9 to both sides:
X² = 9
Take the square root of both sides (remembering to consider both positive and negative square roots):
X = ±3
So the solutions are X = 3 or X = -3.
2) X² + 7 = 0
Subtract 7 from both sides:
X² = -7
This equation has no real solutions because the square of any real number cannot be negative.
3) 3x² = 0
Divide both sides by 3:
x² = 0
Take the square root of both sides:
x = 0
So the solution is x = 0.
4) 1/4x² - 4 = 0
Add 4 to both sides:
1/4x² = 4
Multiply both sides by 4:
x² = 16
Take the square root of both sides:
x = ±4
So the solutions are x = 4 or x = -4.
5) 64b² = 16
Divide both sides by 64:
b² = 16/64
Simplify:
b² = 1/4
Take the square root of both sides:
b = ±1/2
So the solutions are b = 1/2 or b = -1/2.
6) 144 - p² = 0
Add p² to both sides:
144 = p²
Take the square root of both sides:
p = ±12
So the solutions are p = 12 or p = -12.
7) 5z² - 45 = 0
Add 45 to both sides:
5z² = 45
Divide both sides by 5:
z² = 9
Take the square root of both sides:
z = ±3
So the solutions are z = 3 or z = -3.
8) H² = -49
This equation has no real solutions because the square of any real number cannot be negative.
9) 5² - 35 = -35
Perform the calculations:
25 - 35 = -35
Simplify:
-10 = -35
This equation is not true, therefore there are no solutions.
Please let me know if you need further assistance.
To solve each of these equations, we will follow some general steps:
1. Move all terms to one side of the equation, so that one side is equal to zero.
2. If needed, factor the equation if the expression on one side of the equation is a trinomial or a quadratic.
3. Set each factor equal to zero and solve for x or any other variable.
4. Check the solutions by substituting them back into the original equation.
Now let's go through each equation one by one:
1. X² - 9 = 0:
a. Move -9 to the other side: X² = 9.
b. Take the square root of both sides: X = ±√9.
c. Simplify: X = ±3.
2. X² + 7 = 0:
a. Move 7 to the other side: X² = -7.
b. Since there is no real number whose square is negative, this equation has no real solutions.
3. 3x² = 0:
a. Divide both sides by 3: x² = 0.
b. Take the square root of both sides: x = ±√0.
c. Simplify: x = 0.
4. (1/4)x² - 4 = 0:
a. Multiply both sides by 4 to eliminate the fraction: x² - 16 = 0.
b. Factor the equation: (x - 4)(x + 4) = 0.
c. Set each factor equal to zero: x - 4 = 0 or x + 4 = 0.
d. Solve for x: x = 4 or x = -4.
5. 64b² = 16:
a. Divide both sides by 64: b² = 16/64.
b. Simplify: b² = 1/4.
c. Take the square root of both sides: b = ±√(1/4).
d. Simplify: b = ±1/2.
6. 144 - p² = 0:
a. Move 144 to the other side: -p² = -144.
b. Multiply both sides by -1 to switch the signs: p² = 144.
c. Take the square root of both sides: p = ±√144.
d. Simplify: p = ±12.
7. 5z² - 45 = 0:
a. Move -45 to the other side: 5z² = 45.
b. Divide both sides by 5: z² = 45/5.
c. Simplify: z² = 9.
d. Take the square root of both sides: z = ±√9.
e. Simplify: z = ±3.
8. H² = -49:
a. Since there is no real number whose square is negative, this equation has no real solutions.
9. 5² - 35 = -35:
a. Begin by simplifying: 25 - 35 = -35.
b. Continue simplifying: -10 = -35.
c. Since -10 is not equal to -35, this equation has no solutions.
I hope this explanation helps you understand how to solve these equations! Let me know if you have any further questions.