Questions: Solve the equations by factoring show your work. 8x^2 + 2x - 3 = 0

Transcript text: Solve the equations by factoring show your work. 8x^2 + 2x - 3 = 0

Solution

Step 1: Write the Polynomial Equation

We start with the polynomial equation given in the problem:

\[ 8x^2 + 2x - 3 = 0 \]

Step 2: Factor the Polynomial

To solve the equation, we factor the polynomial. The factorization of \(8x^2 + 2x - 3\) is:

\[ (2x - 1)(4x + 3) = 0 \]

Step 3: Solve for \(x\)

Next, we set each factor equal to zero to find the values of \(x\):

For the first factor: \[ 2x - 1 = 0 \implies 2x = 1 \implies x = \frac{1}{2} \]
For the second factor: \[ 4x + 3 = 0 \implies 4x = -3 \implies x = -\frac{3}{4} \]

The solutions to the equation \(8x^2 + 2x - 3 = 0\) are:

\[ \boxed{x = \frac{1}{2}} \quad \text{and} \quad \boxed{x = -\frac{3}{4}} \]

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