x^2 − 10x + 20 = 0
how would u input this answer?
x ^ 2 − 10 x + 20 = 0 Subtact 20 from both sides
x ^ 2 − 10 x + 20 - 20 = 0 - 20
x ^ 2 − 10 x = - 20
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Take one half of the coefficient of x and square it.
In this case [ ( 1 / 2 ) * 10 ] ^ 2 = 5 ^ 2 = 25
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Add 25 to both sides.
x ^ 2 − 10 x + 25 = - 20 + 25
x ^ 2 − 10 x + 25 = 5
factor the lefde hand side.
( x - 5 ) ^ 2 = 5
| x - 5 | = sqrt ( 5 )
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| x - 5 | mean absolute value of x - 5
OR
+ / - ( x - 5 ) = sqrt ( 5 )
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Solutions :
1.
x - 5 = sqrt ( 5 ) Add 5 to both sides
x - 5 + 5 = sqrt ( 5 ) + 5
x = sqrt ( 5 ) + 5
2.
- ( x - 5 ) = sqrt ( 5 )
- x + 5 = sqrt ( 5 ) Subtract 5 to both sides
- x + 5 - 5 = sqrt ( 5 ) - 5
- x = sqrt ( 5 ) - 5 Multiply both sides by - 1
x = - sqrt ( 5 ) + 5
x = 5 - sqrt ( 5 )
This was awesome..you were very thorough!!
"eureka"!! thank you so much
just another question? please...
can you write the answer like this
(x-5)(X+5)?
I SEE NOT..THAT WOULD BE INCORRECT
( x - 5 ) ( x + 5 )=
x * x - x * 5 + 5 * x - 5 * 5 =
x ^ 2 - 5 x + 5 x - 25 =
x ^ 2 - 25 = x ^ 2 - 5 ^ 2
To solve the quadratic equation x^2 - 10x + 20 = 0, you can use the quadratic formula or factorization method. Here's how you could input the answer:
1. Using the Quadratic Formula:
- The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.
In this case:
- a = 1, b = -10, and c = 20.
To input the equation in a mathematical format, you can write:
x = (-(-10) ± √((-10)^2 - 4*1*20)) / (2*1)
Simplifying the equation further:
x = (10 ± √(100 - 80)) / 2
x = (10 ± √20) / 2
Therefore, the answers using the quadratic formula are:
x = (10 + √20) / 2
x = (10 - √20) / 2
2. Using Factorization:
To factorize the quadratic equation x^2 - 10x + 20 = 0, you can look for two numbers that multiply to 20 and add up to -10 (the coefficient of x).
In this case, -2 and -8 are the numbers:
x^2 - 10x + 20 = (x - 2)(x - 8) = 0
Therefore, the answers using factorization are:
x - 2 = 0 => x = 2
x - 8 = 0 => x = 8
So, the equation has two solutions: x = 2 and x = 8.