How do you solve 2x2 - 7x + 3 = 0 by completing the square?

We have to solve \(2x^{2}-7x+3=0\) by completing the square method

Solution

Completing the square method is one of the methods to find the roots of the given quadratic equation.

Steps

Suppose ax2 + bx + c = 0 is the given quadratic equation. Then follow the given steps to solve it by completing the square method.

  • Write the equation in the form, such that c is on the right side.
  • If a is not equal to 1, then divide the complete equation by a, such that co-efficient of x2 is 1.
  • Now add the square of half of the co-efficient of term-x, (b/2a)2, on both the sides.
  • Factorize the left side of the equation as the square of the binomial term.
  • Take the square root on both the sides
  • Solve for variable x and find the roots.
\(2x^{2}-7x+3=0\)

=\(2(x^{2}-\frac{7}{2}x)+3=0\)

=\((x-\frac{7}{4})^{2}=\frac{25}{16}\)

= \((x-\frac{7}{4})= \pm \frac{5}{4}\)

= \(x=\frac{7}{4}\pm \frac{5}{4}=3 or \frac{1}{2}\)

Answer

\(2x^{2}-7x+3=0\)=\(x=\frac{7}{4}\pm \frac{5}{4}=3 or \frac{1}{2}\)

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