Using the quadratic formula, find the solution to x^2 - 6x - 16 = 0.
A. x = -2
B. x = 8
C. x = 8, x = -8
D. x = 8, x = -2
To find the solutions to the quadratic equation x^2 - 6x - 16 = 0 using the quadratic formula, we first need to identify the coefficients in the equation. In this case, the coefficient of x^2 is 1, the coefficient of x is -6, and the constant term is -16.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a represents the coefficient of x^2, b represents the coefficient of x, and c represents the constant term.
Plugging in the values from the given equation, we have:
x = (-(-6) ± √((-6)^2 - 4(1)(-16))) / (2(1))
Simplifying:
x = (6 ± √(36 + 64)) / 2
x = (6 ± √(100)) / 2
x = (6 ± 10) / 2
Now we have two possibilities:
1. x = (6 + 10) / 2 = 16 / 2 = 8
2. x = (6 - 10) / 2 = -4 / 2 = -2
Therefore, the solutions to x^2 - 6x - 16 = 0 are x = 8 and x = -2.
The correct answer is option D. x = 8, x = -2.
To find the solutions to the quadratic equation x^2 - 6x - 16 = 0 using the quadratic formula, follow these steps:
1. Identify the coefficients a, b, and c in the equation. In this case, a = 1, b = -6, and c = -16.
2. Plug these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
3. Substitute the values into the formula:
x = (-(-6) ± √((-6)^2 - 4*1*(-16))) / (2*1)
4. Simplify the equation:
x = (6 ± √(36 + 64)) / 2
5. Continue simplifying:
x = (6 ± √100) / 2
6. Simplify the square root:
x = (6 ± 10) / 2
7. Split the equation into two separate solutions:
x = (6 + 10) / 2 or x = (6 - 10) / 2
8. Simplify each equation:
x = 16/2 or x = -4/2
9. Finalize the solutions:
x = 8 or x = -2
Therefore, the solutions to the equation x^2 - 6x - 16 = 0 are x = 8 and x = -2.
The correct answer is D. x = 8, x = -2.
To find the solution to the quadratic equation x^2 - 6x - 16 = 0 using the quadratic formula, we need to first identify the coefficients in the equation. In this case, the coefficient of x^2 is 1, the coefficient of x is -6, and the constant term is -16.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
where a, b, and c correspond to the coefficients in the quadratic equation. In this case, a = 1, b = -6, and c = -16.
Let's substitute these values in the formula and calculate the roots.
x = (-(-6) ± √((-6)^2 - 4(1)(-16))) / (2(1))
Simplifying further:
x = (6 ± √(36 + 64)) / 2
x = (6 ± √100) / 2
x = (6 ± 10) / 2
Now we have two possibilities:
1. x = (6 + 10) / 2 = 16 / 2 = 8
2. x = (6 - 10) / 2 = -4 / 2 = -2
Therefore, the solutions to the quadratic equation x^2 - 6x - 16 = 0 are x = 8 and x = -2.
The correct answer is:
D. x = 8, x = -2