Corner PatcherArcfolk · quadratics

Patches the missing corner of a square: completing the square.

Complete the Square

Completing the square. In MathBound, the free Algebra I adventure game, Corner Patcher asks these problems, and the only way past is to solve them.

Part of Solving Quadratic Equations: chapter 10 of the standard course.

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Find the Constant. Find the value that makes a binomial a perfect square trinomial by calculating (b/2)^2.
Solve a=1. Solve a quadratic equation with a leading coefficient of 1 and an even middle coefficient by completing the square.
Isolate Variables. Rearrange the equation to isolate the x^2 and x terms on one side before completing the square.

Made by the game’s own question engine. Try each one, then open its steps.

What

constant

completes

the

square

for

x^{2} + 4 x ?

Show the worked steps

Answer: $4$

Solve

by

completing

the

square:

x^{2} - 12 x = - 27

Show the worked steps

$Half$ $of$ $- 12$ $is$ $- 6,$ $and$ $(- 6)^{2} = 36 .$ $Add$ $that$ $to$ $both$ $sides.$
$(x - 6)^{2} = 9 .$
$x - 6 = \pm 3,$ $so$ $x = 9$ $or$ $x = 3 .$

Answer: $x = 9$ $or$ $x = 3$

Rewrite

x^{2} + 4 x + 8

in

the

form

(x + h)^{2} + k .

Show the worked steps

$Half$ $of$ $4$ $is$ $2,$ $so$ $the$ $square$ $is$ $(x + 2)^{2} = x^{2} + 4 x + 4 .$
$So$ $x^{2} + 4 x + 8 = (x + 2)^{2} - 4 + 8 = (x + 2)^{2} + 4 .$

Answer: $(x + 2)^{2} + 4$

Textbook	Lessons
Standard course	10.2
Big Ideas Math Algebra 1	9.4
Big Ideas Math Algebra 1 (2022)	9.4
Carnegie Learning Algebra I	M5 2.4
CPM Core Connections Algebra	8.2.5, 9.1.3
CPS Skyline Algebra	7.3-7.5
enVision Algebra 1	9-5
enVision Algebra 1 (2024)	9-4
Eureka Math Algebra I (EngageNY)	4.11-4.13
Glencoe Algebra 1	9-4
HMH Into Algebra 1	18.2
Holt McDougal Larson Algebra 1	9.5
Illustrative Mathematics Algebra 1	7.11-7.14, 7.15, 7.22-7.23
Illustrative Mathematics Algebra 1 (v.360)	8.11-8.14, 8.15, 8.22-8.23
Math Nation Algebra 1 (Florida B.E.S.T.)	8.5, 8.6, 9.6
OpenStax Elementary Algebra 2e	10.2
Pearson Algebra 1 Common Core	9-5
Reveal Algebra 1	11-5
SpringBoard Algebra 1	32