Using the quadratic formula, find the solution to x2−6x−16=0 .(1 point) Responses x=8, x=−2 x equals 8 , x equals negative 2 x=8, x=−8 x equals 8 , x equals negative 8 x=−2 x equals negative 2 x=8
To find the solution to the quadratic equation x^2 - 6x - 16 = 0, we can use the quadratic formula. The quadratic formula is given as:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = -6, and c = -16. Substituting these values into the quadratic formula, we have:
x = (-(-6) ± √((-6)^2 - 4(1)(-16))) / (2(1))
Simplifying further:
x = (6 ± √(36 + 64)) / 2
x = (6 ± √100) / 2
x = (6 ± 10) / 2
This gives us two possible solutions:
x = (6 + 10) / 2 = 16 / 2 = 8
x = (6 - 10) / 2 = -4 / 2 = -2
Therefore, the solutions to the equation x^2 - 6x - 16 = 0 are x = 8 and x = -2.
To find the solutions to the quadratic equation x^2 - 6x - 16 = 0 using the quadratic formula, follow these steps:
Step 1: Identify the coefficients of the quadratic equation: a = 1, b = -6, and c = -16.
Step 2: Apply the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Step 3: Substitute the values of a, b, and c into the quadratic formula: x = (6 ± √((-6)^2 - 4 * 1 * -16)) / (2 * 1).
Step 4: Simplify the equation inside the square root: x = (6 ± √(36 + 64)) / 2.
Step 5: Simplify further: x = (6 ± √100) / 2.
Step 6: Take the square root of 100: x = (6 ± 10) / 2.
Step 7: Separate the equation to find the two possible answers:
- For x = (6 + 10) / 2: x = 16 / 2 = 8.
- For x = (6 - 10) / 2: x = -4 / 2 = -2.
Therefore, the solutions to the quadratic equation x^2 - 6x - 16 = 0 are x = 8 and x = -2.
To find the solution to the quadratic equation x^2 - 6x - 16 = 0 using the quadratic formula, you need to substitute the coefficients of the equation into the formula and solve for x.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, the equation is in the form ax^2 + bx + c = 0, with coefficients a = 1, b = -6, and c = -16. Substituting these values into the quadratic formula, we have:
x = (-(-6) ± √((-6)^2 - 4(1)(-16))) / (2(1))
x = (6 ± √(36 + 64)) / 2
x = (6 ± √100) / 2
x = (6 ± 10) / 2
Simplifying the expressions inside the square root, we have:
x = (6 ± √100) / 2
x = (6 ± 10) / 2
Now we have two possible solutions:
1. If we use the plus sign:
x = (6 + 10) / 2
x = 16 / 2
x = 8
2. If we use the minus sign:
x = (6 - 10) / 2
x = -4 / 2
x = -2
Therefore, the solutions to the equation x^2 - 6x - 16 = 0 are x = 8 and x = -2.