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$Rewrite the equation by completing the square. {:[2x^(2)-9x+7=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $2x^{2}-9x+7=0$ $\newline$ $(x+\square)^{2}=\square$

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Math Problems

Algebra 1

Solve a quadratic equation by completing the square

Full solution

Q. Rewrite the equation by completing the square.

\newline

2x^{2}-9x+7=0

\newline

(x+\square)^{2}=\square

Given quadratic equation: Start with the given quadratic equation. $2x^2 - 9x + 7 = 0$
Divide by coefficient of x^ $2$ : Divide all terms by the coefficient of x^ $2$ to make the coefficient of x^ $2$ equal to $1$ . $\newline$ $x^2 - \left(\frac{9}{2}\right)x + \left(\frac{7}{2}\right) = 0$
Move constant term to right side: Move the constant term to the right side of the equation. $x^2 - \left(\frac{9}{2}\right)x = -\left(\frac{7}{2}\right)$
Find completing the square number: Find the number that completes the square. This is the square of half the coefficient of $x$ , which is $(\frac{9}{4})^2 = \frac{81}{16}$ .
Add and subtract completing the square number: Add and subtract this number inside the left side of the equation and add it to the right side to maintain equality. $\newline$ $x^2 - \left(\frac{9}{2}\right)x + \left(\frac{81}{16}\right) = \left(\frac{81}{16}\right) - \left(\frac{7}{2}\right)$
Convert right side to common denominator: Convert the right side to have a common denominator before combining the terms. $\newline$ $x^2 - \frac{9}{2}x + \frac{81}{16} = \frac{81}{16} - \frac{56}{16}$
Combine terms on right side: Combine the terms on the right side. $x^2 - \left(\frac{9}{2}\right)x + \left(\frac{81}{16}\right) = \left(\frac{25}{16}\right)$
Write left side as perfect square: Write the left side as a perfect square and simplify the right side. $\newline$ $(x - \frac{9}{4})^2 = \frac{25}{16}$
Rewrite equation in completed square form: Rewrite the equation in the completed square form. $(x - \frac{9}{4})^2 = \frac{25}{16}$