Is this correct:
Solve: (x+5)^2 = 3
I get: x = -5 (+/-) sqrt (3)
Problem #2
Solve: 5(x-2)^2 = 3
I get: x = 3 (+/-) ((sqrt(3))/(5)
No on the second. YOu have take the sqrt5 slso, so
x= 2+- sqrt(3/5)
correct on the first.
To solve the equation (x+5)^2 = 3, you can follow these steps:
1. Expand the expression (x+5)^2 to get x^2 + 10x + 25.
2. Set the expanded expression equal to 3: x^2 + 10x + 25 = 3.
3. Subtract 3 from both sides of the equation: x^2 + 10x + 25 - 3 = 0.
4. Simplify the equation: x^2 + 10x + 22 = 0.
Now, to solve this quadratic equation, you can use the quadratic formula, which states that for an equation in the form of ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a).
In our case, a = 1, b = 10, and c = 22. Plugging these values into the quadratic formula, we get:
x = (-10 ± √(10^2 - 4(1)(22))) / (2(1)).
x = (-10 ± √(100 - 88)) / 2.
x = (-10 ± √12) / 2.
x = -5 ± √3.
Therefore, the correct solution for the equation (x+5)^2 = 3 is x = -5 ± √3.
Now let's move on to the second problem:
To solve the equation 5(x-2)^2 = 3, you can follow these steps:
1. Divide both sides of the equation by 5 to isolate the (x-2)^2 term: (x-2)^2 = 3/5.
2. Take the square root of both sides to eliminate the exponent: √((x-2)^2) = √(3/5).
3. Simplify the square root: x-2 = ±√(3/5).
4. Add 2 to both sides of the equation: x = 2 ± √(3/5).
Therefore, the correct solution for the equation 5(x-2)^2 = 3 is x = 2 ± √(3/5).