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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