Solve using the quadratic formula
X^2-4x=21
Learn the quadratic formula:
x = [-b +/-sqrt(b^2 -4ac)]/2a
In your case a = 1, b = -4 and c = -21
x = [4 +/-sqrt(100)]/2
You finish it. You surely know what the square root of 100 is.
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To solve the equation X^2 - 4x = 21 using the quadratic formula, we first need to rearrange the equation in the standard form ax^2 + bx + c = 0, where a, b, and c are coefficients.
Given the equation X^2 - 4x = 21, we can subtract 21 from both sides to get X^2 - 4x - 21 = 0.
Now, we can identify the coefficients:
a = 1 (coefficient of X^2)
b = -4 (coefficient of x)
c = -21
Next, we can plug these values into the quadratic formula, which is:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values, we get:
x = (-(-4) ± √((-4)^2 - 4(1)(-21))) / (2(1))
x = (4 ± √(16 + 84)) / 2
x = (4 ± √100) / 2
x = (4 ± 10) / 2
Now we have two possibilities, using both the "+" and "-" signs:
Possibility 1:
x = (4 + 10) / 2
x = 14 / 2
x = 7
Possibility 2:
x = (4 - 10) / 2
x = -6 / 2
x = -3
Therefore, the solutions to the equation X^2 - 4x = 21 are x = 7 and x = -3.