206k views
4 votes
Please help me with this question

Starting with the equation
the quadratic formula X =
ax²+bx+c = 0, use completing the square to develop
2
- b ± √b² - 4ac
2a

Please help me with this question Starting with the equation the quadratic formula-example-1

1 Answer

3 votes

To derive the quadratic formula using completing the square, we'll start with the quadratic equation in the form:

ax² + bx + c = 0

Step 1: Move the constant term (c) to the other side of the equation:

ax² + bx = -c

Step 2: Divide the entire equation by 'a' to simplify the equation and make the coefficient of x² equal to 1:

x² + (b/a)x = -c/a

Step 3: To complete the square, take half of the coefficient of 'x', square it, and add it to both sides of the equation. The left side will become a perfect square trinomial:

x² + (b/a)x + (b/2a)² = -c/a + (b/2a)²

Simplifying:

x² + (b/a)x + (b/2a)² = -c/a + (b/2a)²

Step 4: Simplify the right side of the equation:

x² + (b/a)x + (b/2a)² = (-4ac + b²)/(4a²)

Step 5: Factor the left side of the equation as a perfect square:

(x + b/2a)² = (-4ac + b²)/(4a²)

Step 6: Take the square root of both sides:

x + b/2a = ±√((-4ac + b²)/(4a²))

Step 7: Isolate x by subtracting b/2a from both sides:

x = (-b ± √(b² - 4ac))/(2a)

Therefore, the quadratic formula derived using completing the square is:

x = (-b ± √(b² - 4ac))/(2a)

HOPE THIS HELPS :)

User Dayel Ostraco
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories