QuestionAugust 24, 2025

Which number should be added to both sides of this quadratic equation to complete the square? ((-3)/(2))^2+1=x^2-3x+((-3)/(2))^2 Enter the value that belongs in both of these green boxes. ([?])/([ ])+1=x^2-3x+([?])/([ ])

Which number should be added to both sides of this quadratic equation to complete the square? ((-3)/(2))^2+1=x^2-3x+((-3)/(2))^2 Enter the value that belongs in both of these green boxes. ([?])/([ ])+1=x^2-3x+([?])/([ ])
Which number should be added to both sides of this quadratic equation to complete the square? ((-3)/(2))^2+1=x^2-3x+((-3)/(2))^2 Enter the value that belongs in both of these green boxes. ([?])/([ ])+1=x^2-3x+([?])/([ ])

Solution
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Answer

\frac{9}{4} Explanation 1. Identify the quadratic term The equation is x^2 - 3x + \left(\frac{-3}{2}\right)^2. Focus on x^2 - 3x. 2. Calculate the number to complete the square Use the formula \left(\frac{b}{2}\right)^2, where b = -3. So, \left(\frac{-3}{2}\right)^2 = \frac{9}{4}. 3. Add the calculated number to both sides Add \frac{9}{4} to both sides of the equation.

Explanation

1. Identify the quadratic term<br /> The equation is $x^2 - 3x + \left(\frac{-3}{2}\right)^2$. Focus on $x^2 - 3x$.<br /><br />2. Calculate the number to complete the square<br /> Use the formula $\left(\frac{b}{2}\right)^2$, where $b = -3$. So, $\left(\frac{-3}{2}\right)^2 = \frac{9}{4}$.<br /><br />3. Add the calculated number to both sides<br /> Add $\frac{9}{4}$ to both sides of the equation.
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