if Y = X2(xsquared) -6x - 8 find the value(s) of x when y =1.
yes there was a typo its x squared i don't know how to rise the 2
x squared is usually typed like this: x^2 (means x raised to two) :)
anyways, the given in y = x^2 - 6x - 8 and we need to find x when y = 1. thus we substitute y into the equation:
y = x^2 - 6x - 8
1 = x^2 - 6x - 8
now to solve for x,, first we make one side of the equation equal to zero. in this case let's transpose 1 to the right side so that the left side would be zero. to transpose, we take the opposite sign of 1 from positive to negative:
0 = x^2 - 6x - 8 - 1
0 = x^2 - 6x - 9
since it's not factorable, we use the quadratic formula:
x = [-b +- sqrt(b^2 - 4*a*c)]/(2*a)
where
a = numerical coefficient of x^2
b = numerical coefficient of x
c = the constant
note: +- is plus or minus operation
in the equation x^2 - 6x - 9,
a = 1 , b = -6 and c = -9 . substituting:
x = [-(-6) +- sqrt((-6)^2 - 4*(1)*(-9))]/(2*(1))
x = [6 +- sqrt (36 + 36)]/2
x = (6 +- sqrt(72)]/2
x = [6 +- 6*sqrt(2)]/2
now let's split this to + and -
for plus:
x = [6 + 6*sqrt(2)]/2
x = 3 + 3*sqrt(2)
**this is the first root.
for minus:
x = [6 - 6*sqrt(2)]/2
x = 3 - 3*sqrt(2)
**this is the second root.
thus, at y=1, x = 3+3*sqrt(2) and x = 3-3*sqrt(2)
hope this helps~ :)
type x squared as x^2
1 = x^2 - 6x - 8
x^2 - 6x - 9 = 0
Use the quad formula to solve
(I got x = 3 +/-sqrt(2) )
To find the value(s) of x when y = 1 in the equation Y = X^2 - 6x - 8, we can substitute y = 1 and solve for x.
So, we have the equation: 1 = x^2 - 6x - 8
To solve this quadratic equation, we can rearrange it to standard form: x^2 - 6x - 9 = 0
Now, we can solve this equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula because it can solve any quadratic equation.
The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 1, b = -6, and c = -9. Plugging these values into the formula, we get:
x = (-(-6) ± √((-6)^2 - 4*1*(-9))) / (2*1)
= (6 ± √(36 + 36)) / 2
= (6 ± √72) / 2
Simplifying further, we have:
x = (6 ± √(36 * 2)) / 2
= (6 ± 6√2) / 2
Now, we can simplify this expression:
x = 6/2 ± 6√2/2
= 3 ± 3√2
So, the values of x when y = 1 are x = 3 + 3√2 and x = 3 - 3√2.
To solve for the value(s) of x when y = 1 in the equation Y = X^2 - 6x - 8, you can set Y equal to 1 and then solve for x. Here's the step-by-step process to find the value(s) of x:
1. Replace Y with 1 in the equation: 1 = X^2 - 6x - 8.
Now, the equation becomes: X^2 - 6x - 8 = 1.
2. Rearrange the equation in standard form by moving 1 to the other side: X^2 - 6x - 8 - 1 = 0.
Simplify this to: X^2 - 6x - 9 = 0.
3. To solve this quadratic equation, you can either factor it or use the quadratic formula. In this case, the equation does not factor easily, so we will use the quadratic formula.
The quadratic formula is: x = (-b ± √(b^2 - 4ac)) / (2a).
In the equation X^2 - 6x - 9 = 0, we have a = 1, b = -6, and c = -9.
4. Substitute these values into the quadratic formula:
x = (-(-6) ± √((-6)^2 - 4*1*(-9))) / (2*1).
Simplify this to:
x = (6 ± √(36 + 36)) / 2.
x = (6 ± √72) / 2.
5. Further simplify:
x = (6 ± 6√2) / 2.
6. Divide both the numerator and denominator by 2 to simplify:
x = 3 ± 3√2.
Therefore, the value(s) of x when y = 1 in the equation Y = X^2 - 6x - 8 are x = 3 + 3√2 and x = 3 - 3√2.