Please help me with some problems. Thank you!
Solve the equation by square root property.
3. 2x^2 = 26 I don't understand how to solve this problem.
Solve the equation using the quadratic formula.
7. 7x^2=-8x -2 This is what I got x= -8 -or+ square root -8/14
8. 16x^2+1=5x This is what I got x= 5 +or- square root of -39/32
3. divide each side by 2 and then take the square root of both sides
7. a = 7
b = 8
c = 2
8. a = 16
b = -5
c = 1
7. 3132
8. 6400
Sure, I'd be happy to help you with these problems!
For problem 3, 2x^2 = 26, you can solve it by using the square root property. Here's how you can do it:
1. Start by dividing both sides of the equation by 2. This gives you x^2 = 13.
2. Now, take the square root of both sides of the equation. Remember to consider both positive and negative square roots.
The positive square root gives you x = √13.
The negative square root gives you x = -√13.
So the solutions to the equation 2x^2 = 26 are x = √13 and x = -√13.
Now let's move on to problem 7, 7x^2 = -8x - 2. To solve this equation, we can use the quadratic formula. Here's how:
1. First, rearrange the equation to have all terms on one side: 7x^2 + 8x + 2 = 0.
2. Now, identify the values of a, b, and c in the quadratic formula: a = 7, b = 8, and c = 2.
3. Plug in these values into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Substituting the values, we get x = (-8 ± √(8^2 - 4 * 7 * 2)) / (2 * 7).
4. Simplify the expression within the square root: x = (-8 ± √(64 - 56)) / 14.
This simplifies to x = (-8 ± √8) / 14.
The solutions to the equation 7x^2 = -8x - 2 using the quadratic formula are x = (-8 + √8) / 14 and x = (-8 - √8) / 14.
Lastly, for problem 8, 16x^2 + 1 = 5x, we can also use the quadratic formula to solve it. Here's how:
1. Rearrange the equation: 16x^2 - 5x + 1 = 0.
2. Identify the values of a, b, and c: a = 16, b = -5, and c = 1.
3. Plug these values into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Substituting the values, we get x = (-(-5) ± √((-5)^2 - 4 * 16 * 1)) / (2 * 16).
4. Simplify the expression within the square root: x = (5 ± √(25 - 64)) / 32.
This simplifies to x = (5 ± √(-39)) / 32.
Since the expression within the square root is negative, the solutions to the equation 16x^2 + 1 = 5x involve complex numbers. Therefore, we can write the solutions as x = (5 ± √(-39)) / 32.