Solve the equation by using the Quadratic Formula. Round to the nearest tenth, if necessary. Write your solutions from least to greatest, separated by a comma, if necessary. If there are no real solutions, write no solutions. 8x2+12x=8

To solve the quadratic equation $8x^2 + 12x = 8$ using the Quadratic Formula, follow these steps:

1. Rewrite the equation in standard form: The standard form of a quadratic equation is $ax^2 + bx + c = 0$. Start by moving all terms to one side of the equation: $8x^2 + 12x - 8 = 0$

2. Identify the coefficients: In the equation $8x^2 + 12x - 8 = 0$, the coefficients are: $a = 8, \quad b = 12, \quad c = -8$

3. Write down the Quadratic Formula: The Quadratic Formula is given by: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

4. Substitute the coefficients into the formula: $x = \frac{-12 \pm \sqrt{12^2 - 4 \cdot 8 \cdot (-8)}}{2 \cdot 8}$

5. Simplify inside the square root: $x = \frac{-12 \pm \sqrt{144 + 256}}{16}$ $x = \frac{-12 \pm \sqrt{400}}{16}$

6. Simplify the square root: $x = \frac{-12 \pm 20}{16}$

7. Calculate the two possible solutions:

   • For the positive case: $x = \frac{-12 + 20}{16} = \frac{8}{16} = 0.5$
   • For the negative case: $x = \frac{-12 - 20}{16} = \frac{-32}{16} = -2$

8. Write the solutions from least to greatest: $-2, 0.5$

So, the solutions to the equation $8x^2 + 12x = 8$ are $-2$ and $0.5$.