Question

Use the work shown to find the solutions of the quadratic equation.

x2 – x – StartFraction 3 Over 4 EndFraction = 0

x2 – x = StartFraction 3 Over 4 EndFraction

x2 – x + (StartFraction 1 Over 2 EndFraction) squared = StartFraction 3 Over 4 EndFraction + (StartFraction 1 Over 2 EndFraction) squared

x2 – x + StartFraction 1 Over 4 EndFraction = StartFraction 3 Over 4 EndFraction + StartFraction 1 Over 4 EndFraction

Which is a solution of x2 – x – StartFraction 3 Over 4 EndFraction = 0?

Answer 1

Answer:

3 over 2

Step-by-step explanation:

Answer 2

The solution to the quadratic function is 3/2 and 1/2

How to solve quadratic equations using the completing the square method

Given the equation expressed as:

x² - x - 3/4 = 0

Add 3/4 to both sides

x² - x = 3/4

Complete the square to have:

x² - x + 1/4 - 1/4 = 3/4
(x-1/2)² - 1/4 = 3/4
(x-1)² = 3/4 + 1/4
(x-1/2)² = 1
x -1/2 = ±1
x = 1 + 1/2 or 1 - 1/2
x = 3/2 or 1/2

The solution to the quadratic function is 3/2 and 1/2

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