Solve the quadratic equation 3x2 - 5x + 2 = 0 using the quadratic formula x=2a−b±b2−4ac.
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Step-by-Step Solution
Step 1: Identify coefficients
First, we compare the given quadratic equation 3x2−5x+2=0 with the standard form of a quadratic equation, ax2+bx+c=0. By comparing the coefficients, we identify the values for a, b, and c.
Step 2: Substitute into the quadratic formula
Now, we substitute the identified values of a=3, b=−5, and c=2 into the quadratic formula x=2a−b±b2−4ac. This sets up the equation for solving x.
Step 3: Simplify the expression under the square root
We simplify the expression under the square root, which is the discriminant. First, we calculate (−5)2=25 and 4(3)(2)=24. Then, we subtract these values to get 25−24=1.
Step 4: Calculate the square root
The square root of 1 is 1. We replace 1 with 1 in the formula.
Step 5: Find the two possible values for x
Finally, we calculate the two possible values for x. For the first value, we use the plus sign: x1=65+1=66=1. For the second value, we use the minus sign: x2=65−1=64=32.