# Completing the Square

Completing the Square is a fundamental algebraic technique used to solve quadratic equations and manipulate quadratic expressions. By transforming a quadratic expression into a perfect square trinomial, this method enables the easy derivation of key properties such as the vertex form of a quadratic function. This process involves adding and subtracting a carefully chosen constant term to both sides of the equation, resulting in a quadratic expression that can be factored into a squared binomial. Completing the Square plays a crucial role in various mathematical applications, including optimization problems and graphing quadratic functions.

Questions

- How do you solve #x^2 + x + 1=0# by completing the square?
- How do you solve the quadratic #z^2+1=0# using any method?
- How do you solve using the completing the square method #x^2+12x+23=0#?
- How do you solve using the completing the square method # x(x - 2) = 5#?
- How do you solve the quadratic equation by completing the square: #x^2+8x-2=0#?
- How do you solve #2x^2 -12x + 11=0# by completing the square?
- How do you solve #9x^2 - 7x = 12# using completing the square?
- How do you solve by completing the square: #2x^2 - 7x -15 = 0#?
- How do you solve using the completing the square method #3x^2-6x-1=0#?
- How do you solve #4x^2 - x = 0# by completing the square?
- How do you solve #x(x+2)+3=0# by completing the square?
- How do you solve the quadratic equation by completing the square: #x^2 + 4x = 21#?
- How do you solve #x^2=24x+10# by completing the square?
- How do you solve using completing the square method #x^2+5x-2=0#?
- How do you solve #x^2 + 16x = 0# by completing the square?
- How do you solve #x^2+4x+1=0# by completing the square?
- How do you solve the quadratic equation by completing the square: #y^2 + 16y = 2#?
- How do you complete the square to solve #x^2 - 8x + 13 = 0#?
- Is completing the square always the best method?
- How does #t^2-2t-1=0# become #t=1+-sqrt2#?