Solve for "x" using the quadratic formula:
X^2-4x-21=0
x = [4 ± √(16 - 4(1)(-21)]/2
= [4 ± √(16 + 84]/2
= [4 ± √100]/2
= (4 ± 10)/2
= 7,-3
To solve for "x" using the quadratic formula, we will consider the quadratic equation in standard form:
ax^2 + bx + c = 0
In this case, a = 1, b = -4, and c = -21.
The quadratic formula is given as:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values into the formula, we get:
x = (-(-4) ± √((-4)^2 - 4(1)(-21))) / (2(1))
Simplifying further:
x = (4 ± √(16 + 84)) / 2
x = (4 ± √100) / 2
x = (4 ± 10) / 2
This gives us two possible solutions for "x":
Solution 1:
x = (4 + 10) / 2 = 14/2 = 7
Solution 2:
x = (4 - 10) / 2 = -6/2 = -3
Therefore, the solutions for the given quadratic equation x^2 - 4x - 21 = 0 are x = 7 and x = -3.
To solve for "x" using the quadratic formula, we first need to identify the coefficients of the quadratic equation. In this case, the coefficients are:
a = 1
b = -4
c = -21
The quadratic formula states that the solutions for "x" in the equation ax^2 + bx + c = 0 can be found using the following formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the coefficients from the equation X^2 - 4x - 21 = 0 into the quadratic formula, we get:
x = (-(-4) ± √((-4)^2 - 4(1)(-21))) / (2(1))
Simplifying further:
x = (4 ± √(16 + 84)) / 2
x = (4 ± √100) / 2
x = (4 ± 10) / 2
Now we have two possible solutions for "x". By applying both the addition and subtraction operations, we can find the values of "x":
x1 = (4 + 10) / 2
= 14 / 2
= 7
x2 = (4 - 10) / 2
= -6 / 2
= -3
Therefore, the solutions for "x" in the equation X^2 - 4x - 21 = 0 are x = 7 and x = -3.