Students who are searching various sites to learn how to solve quadratic equations using factoring can get them on this page. Here you can find step-by-step explanations for all the questions with related formulas. Before practicing the problems the students must know what is a quadratic equation and a Worksheet on Word Problems on Quadratic Equations by Factoring. This will help you out to score better grades in the exams.
See More:
- Word Problems on Quadratic Equations by Factoring
- Worksheet on Quadratic Formula
- Problems on Quadratic Equations
Quadratic Equations by Factoring Word Problems Worksheet with Answers
Let us discuss the concept of Worksheet on Word Problems on Quadratic Equations by Factoring with explanations in the below section.
Example 1.
The ages of three family children can be expressed as consecutive integers. The square of the age of the youngest child is four more than seven times the age of the oldest child. find the ages of the three children. Show your solution
Solution:
Given,
The ages of three family children can be expressed as consecutive integers.
The square of the age of the youngest child is four more than seven times the age of the oldest child.
Let the ages be x, x + 1, x + 2
x² = 7(x + 2) + 4
x² = 7x + 14 + 4
x² = 7x + 18
x² – 7x – 18 = 0
x² – 9x + 2x – 18 = 0
x(x – 9) + 2(x – 9) = 0
(x + 2)(x – 9) = 0
x + 2 = 0
x = -2
x – 9 = 0
x = 9
Therefore the ages of three children are 9, 10, 11.
Example 2.
The square of a number exceeds the number by 72. Find the number.
Solution:
Given,
The square of a number exceeds the number by 72.
x² = x + 72
Solve x to find the unknown number.
x² – x – 72 = 0
x² – 9x + 8x – 72 = 0
x(x – 9) +8(x – 9) = 0
(x – 9)(x + 8) = 0
x – 9 = 0
x = 9
x + 8 = 0
x = -8
The solution cannot be a negative number so the answer is 9.
Example 3.
Collin is building a deck at the back of his house. He has enough lumber for the deck to be 144 square meters. The length should be 10 meters more than its width.
Solution:
Given,
Collin is building a deck at the back of his house.
He has enough lumber for the deck to be 144 square meters.
The length should be 10 meters more than its width.
Let the width be x
Length be x + 10
Area of deck = 144 square meters
Area of the rectangle = length × width
144 = x(x + 10)
144 = x² + 10x
x² + 10x = 144
x² + 10x – 144 = 0
x² + 18x – 8x – 144 = 0
x(x + 18) – 8 (x + 18) = 0
(x – 8) (x + 18) = 0
x – 8 = 0
x = 8
x + 18 = 0
x = -18
Measurements cannot be a negative number so the value of x is 8.
Width = x = 8 meters
Length = x + 10
8 + 10 = 18 meters
Example 4.
The product of two consecutive negative odd integers is 483. Find the integers.
Solution:
Let the two consecutive odd numbers be x, x + 2.
x(x + 2) = 483
x² + 2x – 483 = 0
x² + 23x – 21x – 483 = 0
x (x + 23) – 21(x + 23) = 0
(x – 21) = 0
x = 21
x + 23 = 0
x = -23
The solution cannot be a negative number so the answer is 21.
x = 21
x + 2 = 21 + 2 = 23
Example 5.
The product of two consecutive odd numbers is 143. Find the integers.
Solution:
Let the two consecutive odd numbers be x, x + 2.
x(x + 2) = 143
x² + 2x = 143
x² + 2x – 143 = 0
x² + 13x – 11x – 143 = 0
x(x + 13) – 11(x + 13) = 0
(x – 11) (x + 13) = 0
x – 11 = 0
x = 11
x + 13 = 0
x = -13
Example 6.
The product of two consecutive even integers is 528. Find the integers.
Solution:
Given,
The product of two consecutive even integers is 528.
Let the two consecutive even integers be x + 2 and x + 4.
(x + 2)(x + 4) = 527
x² + 4x + 2x + 8 = 528
x² + 6x + 8 = 528
x² + 6x + 8 – 528 = 0
x² + 6x – 520 = 0
Example 7.
The product of two consecutive odd integers is 255. Find the integers.
Solution:
Given,
The product of two consecutive odd integers is 255.
Let the two consecutive positive odd integers be x, x + 2
x(x + 2) = 255
x² + 2x = 255
x² + 2x – 255 = 0
x² + 17x – 15x – 255 = 0
x(x + 17) -15(x + 17) = 0
(x + 17) (x – 15) = 0
x + 17 = 0
x = -17
x – 15 = 0
x = 15
x = 15
x + 2 = 15 + 2 = 17
Thus the two consecutive integers are 15, 17.
Example 8.
Solve the following quadratic equation, x² = -7x – 10, selecting a method that we learned, and state why you chose that method.
Solution:
Given the equation x² = -7x – 10
x² + 7x + 10 = 0
x² + 5x + 2x + 10 = 0
x(x + 5) + 2(x + 5) = 0
(x + 2) (x + 5) = 0
x + 2 = 0
x = -2
x + 5 = 0
x = -5