use the quadratic formula to solve this equation.
4x^2-8x+3=5
use the formula x=-b + or - the sqrt of b^2-4ac/2a
yes, the 2a divides into all. Memorize it.
To solve the quadratic equation 4x^2 - 8x + 3 = 5 using the quadratic formula, you can follow these steps:
Step 1: Identify the values of a, b, and c in the given equation.
- In this case, a = 4, b = -8, and c = (3 - 5) = -2.
Step 2: Substitute the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Step 3: Simplify the quadratic formula:
x = (-(-8) ± √((-8)^2 - 4 * 4 * (-2))) / (2 * 4)
Step 4: Continue simplifying:
x = (8 ± √(64 + 32)) / 8
x = (8 ± √(96)) / 8
Step 5: Simplify the square root:
x = (8 ± √(16 * 6)) / 8
x = (8 ± 4√6) / 8
Step 6: Divide both the numerator and denominator by 4:
x = 2 ± (√6 / 2)
So, the solutions to the given equation are:
x = 2 + (√6 / 2)
x = 2 - (√6 / 2)
Remember, when applying the quadratic formula, it is essential to correctly substitute the values of a, b, and c and properly simplify the expression to obtain the correct solution.