Final answer:
The equation 8z² + 18z - 7 = -2 is solved by first bringing it to the standard quadratic form, which is 8z² + 18z - 5 = 0. Then, the quadratic formula is applied using the coefficients a = 8, b = 18, and c = -5 to find z's values. Simplifying the results will give the final solutions.
Step-by-step explanation:
To solve the equation 8z² + 18z - 7 = -2 using the quadratic formula, we first need to rearrange the equation to get 0 on one side. This gives us 8z² + 18z - 5 = 0. Now we can apply the quadratic formula. For an equation of the form az² + bz + c = 0, the formula is z = (-b ± √(b² - 4ac)) / (2a). Substituting the appropriate values from our equation:
We then calculate the discriminant (δ = b² - 4ac) which is 18² - 4 × 8 × (-5) and find its value. After that, we substitute the values of a, b, and δ back into the quadratic formula to find the two possible values for z. Finally, we simplify the expressions to get the answers in their simplest form.
Eliminate terms wherever possible to simplify the algebra, and check the answer to see if it is reasonable.