Solve the quadratic equation: 2x2 - 7x + 3 = 0
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Step-by-Step Solution
Step 1: Identify coefficients
We first identify the coefficients a, b, and c from the given quadratic equation 2x2−7x+3=0. These coefficients are essential for applying the quadratic formula.
Step 2: Apply the quadratic formula
The quadratic formula is used to find the roots of any quadratic equation in the form ax2+bx+c=0. This formula provides a direct method to solve for x.
Step 3: Substitute values into the formula
Now we substitute the values of a=2, b=−7, and c=3 into the quadratic formula. Careful substitution helps prevent errors in calculation.
Step 4: Simplify the expression under the square root
We calculate the terms inside the square root. (−7)2 becomes 49, and 4(2)(3) becomes 24. The denominator 2(2) becomes 4.
Step 5: Calculate the square root
Subtracting 24 from 49 gives 25. The square root of 25 is 5. We now have a simplified expression ready for finding the two possible values of x.
Step 6: Calculate the two possible values for x
The ± sign indicates two solutions. We calculate one root using the positive sign and the other root using the negative sign.
Step 7: Final calculation of roots
Performing the final division, we find the two roots of the quadratic equation. The first root is 3 and the second root is 1/2.