How do I solve this quadratic equation using the quadratic formula "8a(squared)-a+2=0"
8a^2-a+2 = 0
x = (1±√(1^2-4*8*2)]/(2*8) = (1±√-63)/16 = (1±3√7 i)/16
To solve the quadratic equation 8a^2 - a + 2 = 0 using the quadratic formula, follow these steps:
Step 1: Identify the coefficients a, b, and c in the equation ax^2 + bx + c = 0.
In this equation, the coefficient of a^2 term (a) is 8, the coefficient of the a term (b) is -1, and the constant term (c) is 2.
Step 2: Substitute the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 8, b = -1, and c = 2, so the formula becomes:
x = (-(-1) ± √((-1)^2 - 4(8)(2))) / (2(8))
Solving this equation will give us the solutions for the quadratic equation.
Step 3: Simplify the equation inside the square root:
x = (1 ± √(1 - 64)) / 16
x = (1 ± √(-63)) / 16
Step 4: Determine the nature of the solutions based on the discriminant (b^2 - 4ac).
In this case, the discriminant is (-1)^2 - 4(8)(2) = 1 - 64 = -63. Since the discriminant is negative, the quadratic equation has no real solutions.
Step 5: Write the final answer:
The equation 8a^2 - a + 2 = 0 has no real solutions.