The 8-2x under the square root -x =0 someone help
again, i think i'd look at the quadratic equation.
post back if you don't know what this is and i'll give you an alternative.
i do know that it is the b + or - the square root of b squared -4ac over 2a but I still can't get the correct answer
i get -4 and 2. is that what you got?
Since you squared both sides of the equation while solving, any answer MUST be verified
if x = 2
left side = √(8-4) - 2
= 2-2
= 0
= right side
if x = -4
left side = √(8+8) - (-4)
= 4 + 4 = 8 which is not the right side
so x = 2 is the only solution
To find the value(s) of x that satisfy the equation √(-x) = 8 - 2x, you can follow these steps:
1. Begin by isolating the square root on one side of the equation. Square both sides of the equation to remove the square root symbol:
(√(-x))^2 = (8 - 2x)^2
Simplifying, you have:
-x = (8 - 2x)^2
2. Expand the right side of the equation:
-x = (8 - 2x)(8 - 2x)
= 64 - 16x - 16x + 4x^2
= 64 - 32x + 4x^2
3. Rearrange the equation to bring all terms to one side, making it a quadratic equation:
4x^2 - 32x + 64 - x = 0
4. Combine like terms:
4x^2 - 33x + 64 = 0
5. At this point, you can solve the quadratic equation. You can either factor it, complete the square, or use the quadratic formula. Let's use the quadratic formula:
Given a quadratic equation of the form ax^2 + bx + c = 0, the roots x can be calculated using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Applying this to our equation, where a = 4, b = -33, and c = 64:
x = (-(-33) ± √((-33)^2 - 4 * 4 * 64)) / (2 * 4)
Simplifying further:
x = (33 ± √(1089 - 1024)) / 8
x = (33 ± √65) / 8
The solutions for x are:
x = (33 + √65) / 8 ~ 1.356
x = (33 - √65) / 8 ~ 7.644
Therefore, the values of x that satisfy the equation √(-x) = 8 - 2x are approximately 1.356 and 7.644.