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
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