Find all real solutions. SR (x^2+3x+6)=4
Y = x^2 + 3x + 6 = 4
Y = x^2 + 3x + 6-4 = 0
x^2 3x + 2 = 0
C = 2 = 1*2.
(x+1)(x+2) = 0
x+1 = 0
X = -1.
x+2 = 0
x = -2
To find all the real solutions to the equation SQRT(x^2 + 3x + 6) = 4, we need to solve the equation by isolating x.
Here's how you can do it:
1. Start by squaring both sides of the equation to eliminate the square root sign.
(SQRT(x^2 + 3x + 6))^2 = 4^2
Simplifying this gives us:
x^2 + 3x + 6 = 16
2. Rearrange the equation to bring all terms to one side, resulting in a quadratic equation:
x^2 + 3x + 6 - 16 = 0
x^2 + 3x - 10 = 0
3. Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring.
The quadratic equation factors as:
(x + 5)(x - 2) = 0
4. Set each factor equal to zero and solve for x:
x + 5 = 0 or x - 2 = 0
x = -5 or x = 2
So, the real solutions to the equation SR(SQRT(x^2 + 3x + 6) = 4) are x = -5 and x = 2.