Final answer:
To solve the quadratic equation 8x² - 55x - 7 = 0, use the quadratic formula. The solutions to the equation are x = 0.8125 and x = -1.5625.
Step-by-step explanation:
To solve the quadratic equation 8x² - 55x - 7 = 0, we can use the quadratic formula. For an equation of the form ax² + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a = 8, b = -55, and c = -7. Substituting these values into the formula, we get:
x = (-(-55) ± √((-55)² - 4(8)(-7))) / (2(8))
Simplifying the equation, we have:
x = (55 ± √(3025 + 224)) / 16
x = (55 ± √(3249)) / 16
x = (55 ± 57) / 16
Therefore, the solutions to the equation are x = 0.8125 and x = -1.5625.