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Which equation is equivalent to the given equation?
X^2-6x=8

1 Answer

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Answer: The equation that is equivalent to X^2 - 6x = 8 is X = 3 ± √17.

Explanation:

To find an equation equivalent to the given equation X^2 - 6x = 8, we can manipulate the equation using algebraic operations.

1. Move the constant term to the other side of the equation:

X^2 - 6x - 8 = 0

2. To find the equation that is equivalent to this quadratic equation, we can either factor it or use the quadratic formula.

Option 1: Factoring

By factoring the quadratic equation, we can express it as the product of two binomials:

(X - a)(X - b) = 0

To find a and b, we need to determine two numbers whose product is -8 and whose sum is -6 (the coefficient of x).

In this case, the numbers are -2 and -4:

(X - 2)(X - 4) = 0

Therefore, the equation that is equivalent to X^2 - 6x = 8 is (X - 2)(X - 4) = 0.

Option 2: Quadratic formula

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

X = (-b ± √(b^2 - 4ac)) / 2a

For the given equation X^2 - 6x - 8 = 0, a = 1, b = -6, and c = -8.

Plugging these values into the quadratic formula, we get:

X = (-(-6) ± √((-6)^2 - 4(1)(-8))) / (2(1))

Simplifying further:

X = (6 ± √(36 + 32)) / 2

X = (6 ± √68) / 2

X = (6 ± 2√17) / 2

X = 3 ± √17

Both (X - 2)(X - 4) = 0 and X = 3 ± √17 are equivalent equations to X^2 - 6x = 8.

User Igor Golodnitsky
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