Solving Quadratic Equations: Completing the Square

Presentation

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Mathematics

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9th Grade

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Practice Problem

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Medium

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CCSS

HSA-REI.B.4B

Standards-aligned

Shana Speicher

Used 75+ times

FREE Resource

10 Slides • 7 Questions

Solving Quadratic Equations: Completing the Square

Complete the Square

Find the "Magic Number"

Start with the "b" value, divide by 2, then square it

6 / 2 = 3 and 3*3 = 9

Balance the equation by adding the "magic number" to both sides.

Steps to solve a quadratic equation using the process of completing the square.

Solve the equation: $x^2+8x-9=0$

Isolate the constant: x^2 + 8x = 9
Find the "magic number" to form a perfect square: 8 / 2 = 4, 4^2 = 16
Add 16 to both sides: x^2 + 8x + 16 = 9 + 16
Write the trinomial as a binomial squared: (x + 4)^2 = 25
Square root both sides: x + 4 = (pos/neg) 5
Solve the equation: x = -4 plus/minus 5
Simplify: -4 + 5 = 1, -4 - 5 = -9

Another example

An example where "b" is ODD.

Example with an irrational solution

Analyzing Solutions

The sum of a rational number and an irrational number is always irrational.

Example where "b" is odd and the solution is irrational.

Fill in the Blanks

$x^2+10x+c$
What value of "c" will make this a perfect square trinomial?

Type answer...

Fill in the Blanks

$x^2-20x=5$

What number would you add to both sides of the equation to complete the square?

Type answer...

Multiple Select

$x^2+12x=-20$

Solve the equation by completing the square. Check the solution(s).

x = -4

x = -2

x = 4

x = 2

x = -10

Multiple Choice

$x^2+8x\ =\ 33$

Solve the equation by completing the square. Which is the solution set of the equation?

{-11, 3}

{-3, 11}

{-4, 4}

{-7, 7}

Multiple Choice

Complete the work shown. Which describes the solutions of the equation?

Since 7 and 11 are both rational, the sum and difference are rational.

Since 14 and 11 are both rational, the sum and difference are rational.

Since 7 is rational and is irrational, the sum and difference are irrational.

Since is irrational and 11 is rational, the sum and difference are irrational.

Multiple Choice

$x^2-10=30x$

Solve the quadratic equation by completing the square.

{-220, 250}

{-250, 220}

$15\pm\sqrt{235}$

$-15\pm\sqrt{235}$

Multiple Choice

$x^2=8-5x$

Solve the quadratic equation by completing the square.

$\frac{5\pm\sqrt{57}}{2}$

$\frac{-5\pm\sqrt{57}}{2}$

$-\frac{47}{4},\ \frac{67}{4}$

$-\frac{67}{4},\ \frac{47}{4}$

Solving Quadratic Equations: Completing the Square

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