using quadratic formula solve
|x^2-2x-6| = 4. and answer have to be 1+-sqrt3, 1+-sqrt11 i just not get how to get this.
| x ^ 2 - 2 x - 6 |= 4
Eliminate the absolute value :
x ^ 2 - 2 x - 6 = 4
OR
x ^ 2 - 2 x - 6 = - 4
Your must solve both equations.
In google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type:
x ^ 2 - 2 x - 6 = 4
and click option: solve it!
You will see solutions of equation :
x ^ 2 - 2 x - 6 = 4
step-bay-step
Then in rectangle type:
x ^ 2 - 2 x - 6 = - 4
and click option: solve it!
You will see solutions of equation :
x ^ 2 - 2 x - 6 = - 4
step-bay-step
Equation :
| x ^ 2 - 2 x - 6 | = 4
has 4 solutions :
1 + sqrt ( 11 )
1 - sqrt ( 11 )
1 + sqrt ( 3 )
and
1 - sqrt ( 3 )
To solve the equation |x^2 - 2x - 6| = 4 using the quadratic formula, we need to follow these steps:
1. Rewrite the equation without the absolute value sign:
x^2 - 2x - 6 = ±4
2. Solve the equation when the expression inside the absolute value is equal to 4:
x^2 - 2x - 6 = 4
Rearrange the equation in standard quadratic form:
x^2 - 2x - 10 = 0
3. Apply the quadratic formula to solve for x:
The quadratic formula is: x = (-b ± sqrt(b^2 - 4ac)) / (2a)
In the equation x^2 - 2x - 10 = 0, the values of a, b, and c are:
a = 1, b = -2, c = -10
4. Substitute these values into the quadratic formula and simplify:
x = (-(-2) ± sqrt((-2)^2 - 4(1)(-10))) / (2(1))
x = (2 ± sqrt(4 + 40)) / 2
x = (2 ± sqrt(44)) / 2
x = 1 ± sqrt(11)
We have obtained the two possible solutions: x = 1 + sqrt(11) and x = 1 - sqrt(11).
5. Now let's solve the equation when the expression inside the absolute value is equal to -4:
x^2 - 2x - 6 = -4
Rearrange the equation:
x^2 - 2x - 6 + 4 = 0
x^2 - 2x - 2 = 0
6. Apply the quadratic formula to solve for x:
Using the values a = 1, b = -2, and c = -2:
x = (-(-2) ± sqrt((-2)^2 - 4(1)(-2))) / (2(1))
x = (2 ± sqrt(4 + 8)) / 2
x = (2 ± sqrt(12)) / 2
x = 1 ± sqrt(3)
We have obtained the two possible solutions: x = 1 + sqrt(3) and x = 1 - sqrt(3).
Thus, the solutions to the given equation are x = 1 + sqrt(11), x = 1 - sqrt(11), x = 1 + sqrt(3), and x = 1 - sqrt(3).