To solve for x using the quadratic formula, we first need to rewrite the equation in the standard form of a quadratic equation: ax^2 + bx + c = 0.
Given equation: x^2 - 4x = 21
Rearranging terms: x^2 - 4x - 21 = 0
Now, we can see that a = 1, b = -4, and c = -21.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in the values of a, b, and c into the formula:
x = (4 ± √((-4)^2 - 4*1*(-21))) / 2*1
x = (4 ± √(16 + 84)) / 2
x = (4 ± √100) / 2
x = (4 ± 10) / 2
This gives two possible solutions for x:
x = (4 + 10) / 2 = 14 / 2 = 7
x = (4 - 10) / 2 = -6 / 2 = -3
Therefore, the solutions of the equation x^2 - 4x = 21 are x = 7 and x = -3, which corresponds to option C: -3, 7.
What are the solutions of x^2−4x=21? Use the quadratic formula.
A. -3, -7
B. 3, 7
C. -3, 7
D. 3, -7
1 answer
1 answer