What are the solutions of 8x2 = 6 + 22x?
Solving the Quadratic Equation
When solving a quadratic equation, the goal is to find the values of the variable that make the equation true. In this case, we are given the equation 8x2 = 6 + 22x. To solve for x, we need to rearrange the equation into the standard form of a quadratic equation, which is ax2 + bx + c = 0.
Rearranging the Equation
Let's rearrange the given equation 8x2 = 6 + 22x by moving all terms to one side:
8x2 - 22x - 6 = 0
Factoring the Quadratic Equation
Now, we need to factor the quadratic equation 8x2 - 22x - 6 = 0 to solve for x. Factoring gives us:
2(4x2 - 11x - 3) = 0
2(4x + 1)(x - 3) = 0
Finding the Solutions
From the factored form, we can see that the solutions for x are:
x = -1/4 or x = 3
What are the solutions of 8x2 = 6 + 22x? Check all of the boxes that apply. x = -1/4, x = 3