.
It can be solved by completing the square method
x^2 - 10x + 24 = 0
(x^2 - 2*5x + 25) - 25 + 24 = 0
(x-5)^2 - 1 = 0
(x-5)^2 = 1
x-5 = +/- 1 (after taking square root from both sides)
x = 5 +/- 1.
ANSWER. The given equation has two solutions. One solution is 5-1 = 4.
Other solution is 5+1 = 6.
Alternatively, it can be solved by factoring
x^2 - 10x + 24 = 0
(x-4)*(x-6) = 24 <<<---=== factoring is made MENTALLY in your head.
giving the same roots 4 and 6.
Solved in two ways for your better understanding.
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If you want to see many other similar and different problems on solving quadratic equations,
look into the lessons
- Introduction into Quadratic Equations
- PROOF of quadratic formula by completing the square
- HOW TO complete the square - Learning by examples
- HOW TO solve quadratic equation by completing the square - Learning by examples
- Solving quadratic equations without quadratic formula
in this site.
You will find there many problems, solved using the quadratic formula, completing the square and factoring.
Learn the subject from there and become an expert in the area.
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