Question

Complete the square to form a true equation;
x^2-3/4x+__ = (x-__)^2

Answer 1

To complete the square for x^2 - \frac{3}{4}x, add \frac{9}{64} to both sides resulting in (x - \frac{3}{8})^2.

Step-by-step explanation:

To complete the square for the given quadratic expression x^2 - \frac{3}{4}x, we must find a value to fill in the blank that will allow us to express the equation in the form of (x - a)^2. We do this by taking (\frac{b}{2a})^2 where a is the coefficient of x^2 (which is 1 in this case) and b is the coefficient of x (which is -\frac{3}{4}). Therefore, we have (\frac{-\frac{3}{4}}{2 \cdot 1})^2 = (\frac{-\frac{3}{4}}{2})^2 = (\frac{-\frac{3}{8}}{1})^2 = (\frac{3}{8})^2 = \frac{9}{64}.

So, the completed square equation is x^2 - \frac{3}{4}x + \frac{9}{64} = (x - \frac{3}{8})^2. The term you fill in the blank with is \frac{9}{64}, and the term to fill in the second blank in the expression on the right side of the equation is \frac{3}{8}.

Answer 2

Answer: x² - (3/4)x + 9/64 = (x + 3/8)²

Step-by-step explanation:

Concept:

Here, we need to know the idea of completing the square.

Completing the square is a technique for converting a quadratic polynomial of the form ax²+bx+c to the form (x-h)²for some values of h.

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

If we expand (x - h)² = x² - 2 · x · h + h²

Given equation:

• x² - (3/4)x +___ = (x - __)²

Since [x² - (3/4)x +___] is the expanded form of (x - h)², then (-3/4)x must be equal to 2 · x · h. Thus, we would be able to find the value of h.

• (-3/4) x = 2 · x · h ⇔ Given
• -3/4 = 2 · h ⇔ Eliminate x
• h = -3/8 ⇔ Divide 2 on both sides

Finally, we plug the final value back to the equation.

• x² - 2 · x · h + h² = (x - h)²
• x² - (3/4)x + (-3/8)² = (x + 3/8)²
• x² - (3/4)x + 9/64 = (x + 3/8)²

Hope this helps!! :)

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