Is This the Right Way to Solve a Quadratic Equation?

  • Context: MHB 
  • Thread starter Thread starter Casio1
  • Start date Start date
  • Tags Tags
    Quadratic
Click For Summary
SUMMARY

The discussion confirms that the method used to solve the quadratic equation 2(x - 5)² = 32 is valid. The participant correctly divided both sides by 2, resulting in (x - 5)² = 16, and then took the square root to find the roots x = 9 and x = 1. Additionally, an alternative method using the difference of squares was presented, leading to the same solutions. Both approaches are accepted as correct and effective for solving quadratic equations.

PREREQUISITES
  • Understanding of quadratic equations and their standard forms
  • Knowledge of algebraic operations, including division and square roots
  • Familiarity with the difference of squares factorization technique
  • Basic skills in solving equations
NEXT STEPS
  • Study the quadratic formula for solving equations of the form ax² + bx + c = 0
  • Learn about completing the square as an alternative method for solving quadratics
  • Explore the concept of discriminants to determine the nature of roots
  • Practice solving more complex quadratic equations using various methods
USEFUL FOR

Students learning algebra, educators teaching quadratic equations, and anyone looking to improve their problem-solving skills in mathematics.

Casio1
Messages
86
Reaction score
0
Hi everyone(Wink)

I have an equation which looks like quadratic to me.

2(x - 5)2 = 32

Can I divide both sides by 2?

(x - 5)2 = 16

Can I take the square root?

x - 5 = + or - 4

if x = 5 plus 4 = 9

if x = 5 - 4 = 1

Therefore my roots would be;

x = 9 or x = 1

Is this method acceptable and the correct way to find the values of x. I know it works out OK but am wondering about the way I have done it?

Thanks
 
Mathematics news on Phys.org
Hi Casio!

(Yes) Well done. That's exactly how you should do this problem every step of the way.
 
Yes, that is a perfectly valid procedure. All of your steps are correct. (Nod)
 
After dividing by 2, we may also arrange as the difference of squares:

(x - 5)2 - 42 = 0

((x - 5) + 4)((x - 5) - 4) = 0

(x - 1)(x - 9) = 0

x = 1, 9
 

Similar threads

MHB Quadratic equations intersaction point is minimum instead of roots
  • · Replies 2 ·
Replies
2
Views
1K
MHB Solving 8 Roots: Can 3 Quadratic Polynomials Fulfill $f(g(h(x)))=0$?
  • · Replies 1 ·
Replies
1
Views
1K
MHB [ASK] Proof of Some Quadratic Functions
  • · Replies 6 ·
Replies
6
Views
2K
High School Complete the square, yes, but what does it mean?
  • · Replies 19 ·
Replies
19
Views
3K
MHB (Seemingly) Random Sequences
  • · Replies 7 ·
Replies
7
Views
2K
MHB Which Quadratic Function Has Exactly One X-Intercept?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Quartic real roots - factor part into quadratic
  • · Replies 3 ·
Replies
3
Views
1K
High School Need assistance with an unusual quadratic solution method
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Quadratic, cubic, quartic, quintic equations
  • · Replies 16 ·
Replies
16
Views
5K
MHB Do 1 + √5 and 1 - √5 Solve the Equation x² - 2x - 4 = 0?
  • · Replies 3 ·
Replies
3
Views
2K