Weaver Cole
06/21/2023 · Primary School

Jecide what number must be added to both sides of the equation to make the left side a perfect squa \( x^{2}-6 x=3 \) Add a number to both sides of the equation to make the left side a perfect square trinomial. \( x^{2}-6 x+9=3+9 \) (Simplify your answers.) Factor the left side of the equation and simplify the right side. \( (\square)^{2}=\square \) (Simplify your answers.)

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Step-by-step Solution

To make the left side of the equation \( x^2 - 6x = 3 \) a perfect square trinomial, we need to complete the square. 1. Start with the equation: \[ x^2 - 6x = 3 \] 2. To complete the square, take half of the coefficient of \( x \) (which is \(-6\)), square it, and add it to both sides. Half of \(-6\) is \(-3\), and squaring it gives \(9\). 3. Add \(9\) to both sides: \[ x^2 - 6x + 9 = 3 + 9 \] This simplifies to: \[ x^2 - 6x + 9 = 12 \] 4. Now, the left side can be factored as a perfect square: \[ (x - 3)^2 = 12 \] So, the completed steps are: - The number added to both sides is \(9\). - The factored form is: \[ (x - 3)^2 = 12 \]

Quick Answer

Add \(9\) to both sides to make the left side a perfect square trinomial. The factored form is \((x - 3)^2 = 12\).
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