Get the answer to "How to solve 2x2-7x+3=0 by completing the square."

inimigurhkg

Answered question

2023-02-25

How to solve

2 x^{2} - 7 x + 3 = 0

by completing the square.

Answer & Explanation

Cailyn Knight

Beginner2023-02-26Added 7 answers

Calculate the quadratic equation's roots.
Given:

2 x^{2} - 7 x + 3 = 0

\Rightarrow

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

Making a perfect square by adding and subtracting

2 {(\frac{7}{4})}^{2}

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

\Rightarrow

2 {(x - \frac{7}{4})}^{2} - \frac{49}{8} + 3 = 0

\Rightarrow

2 {(x - \frac{7}{4})}^{2} = \frac{25}{8}

\Rightarrow

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

\Rightarrow

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

\Rightarrow

x = \pm \frac{5}{4} + \frac{7}{4}

\Rightarrow

x = 3 o r \frac{1}{2}

Hence, the roots of

2 x^{2} - 7 x + 3 = 0

are

3

and

\frac{1}{2} .

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