Using the quadratic formula to solve for x in the equation x2 = 7x + 8 results in what value(s)?
Do you know the quadratic formula? What don't you understand about it?
To solve the equation x^2 = 7x + 8 using the quadratic formula, we first need to rewrite the equation in the form ax^2 + bx + c = 0.
In this case, the equation is already in that form, with a = 1, b = -7, and c = -8.
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).
Plugging in the values from our equation, we have x = (7 ± √((-7)^2 - 4(1)(-8))) / (2(1)).
Simplifying the expression under the square root gives us x = (7 ± √(49 + 32)) / 2.
Further simplifying gives us x = (7 ± √81) / 2.
Taking the square root of 81 gives us x = (7 ± 9) / 2.
So, we have two possible solutions:
- x = (7 + 9) / 2 = 16 / 2 = 8
- x = (7 - 9) / 2 = -2 / 2 = -1
Therefore, the values of x that solve the equation x^2 = 7x + 8 are x = 8 and x = -1.