Solve for x: 2x2 - 7x + 3 = 0. I am a class 10 student, please help me understand how to do it.
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Step-by-Step Solution
Step 1: Identify coefficients
The given equation is 2x2−7x+3=0. This is a quadratic equation in the standard form ax2+bx+c=0. By comparing the given equation with the standard form, we can identify the coefficients a, b, and c.
Step 2: Apply the quadratic formula
Now that we have the values of a, b, and c, we can use the quadratic formula to find the values of x. The quadratic formula provides the solutions for any quadratic equation.
Step 3: Substitute values into the formula
Substitute the identified values a=2, b=−7, and c=3 into the quadratic formula. Be careful with the signs, especially for the term −b.
Step 4: Simplify the expression
First, calculate the term inside the square root, which is the discriminant b2−4ac. Then, simplify the square root and the denominator.
Step 5: Calculate the two possible values for x
The ± sign in the quadratic formula indicates that there are two possible solutions for x. Calculate each solution separately, one using the plus sign and the other using the minus sign.
Step 6: Final solutions
Perform the final division for both expressions to get the two solutions for x. These are the roots of the quadratic equation.