Using the quadratic formula, find the solution to x^2 – 6x – 16 = 0
To find the solution to the quadratic equation x^2 – 6x – 16 = 0, we will make use of the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In the given equation, a = 1, b = -6, and c = -16.
Plugging these values into the quadratic formula, we have:
x = (-(-6) ± √((-6)^2 - 4(1)(-16)))/(2(1))
= (6 ± √(36 + 64))/2
= (6 ± √100)/2
= (6 ± 10)/2
Now we have two possible solutions:
1. When x = (6 + 10)/2 = 16/2 = 8
2. When x = (6 - 10)/2 = -4/2 = -2
Hence, the solutions to the equation x^2 – 6x – 16 = 0 are x = 8 and x = -2.
Step 1: Identify the coefficients a, b, and c from the quadratic equation: x^2 - 6x - 16 = 0
In this case, a = 1, b = -6, and c = -16.
Step 2: Substitute the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Step 3: Calculate the discriminant (b^2 - 4ac):
Discriminant = (-6)^2 - 4 * 1 * (-16)
Discriminant = 36 + 64
Discriminant = 100
Step 4: Determine the solutions by substituting the values of a, b, and c into the quadratic formula:
x = (-(-6) ± √(100)) / (2 * 1)
x = (6 ± 10) / 2
Step 5: Calculate the two possible solutions:
Solution 1: x = (6 + 10) / 2
x = 16 / 2
x = 8
Solution 2: x = (6 - 10) / 2
x = -4 / 2
x = -2
Therefore, the solutions to the quadratic 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, we'll use the formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this equation, a, b, and c are the coefficients of the quadratic equation. Comparing the given equation with the standard form ax^2 + bx + c = 0, we have:
a = 1, b = -6, and c = -16
Plugging these values into the quadratic formula, we get:
x = (-(-6) ± sqrt((-6)^2 - 4(1)(-16))) / (2(1))
Simplifying further:
x = (6 ± sqrt(36 + 64)) / 2
x = (6 ± sqrt(100)) / 2
x = (6 ± 10) / 2
Now we have two possible solutions:
x1 = (6 + 10) / 2 = 16 / 2 = 8
x2 = (6 - 10) / 2 = -4 / 2 = -2
Therefore, the solutions to the equation x^2 - 6x - 16 = 0 are x = 8 and x = -2.