k asked in Science & MathematicsMathematics · 2 months ago

# What are the two answers to Sqrt 3x = x-6 ?

There should be two values of x, but only one of them solves the equation.

If possible, please show work so I can use the example for more of these problems

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• 2 months ago

√(3x) = x - 6

(√(3x))² = (x - 6)²

3x = x² - 12x + 36

x² - 15x + 36 = 0

(x - 3)(x - 12) = 0

x - 3 = 0 or x - 12 = 0

x = 3 or x = 12

Check:

When x = 3:

L.H.S. = √(3*3) = 3

R.H.S. = 3 - 6 = -3

Since L.H.S. ≠ R.H.S., reject x = 3

When x = 12:

L.H.S. = √(3*12) = 6

R.H.S. = 12 - 6 = 6

L.H.S. = R.H.S., accept x = 3

• 2 months ago

Same advice. Learn to use parentheses. see the solutions to what you meant. [Technically the left side reads "compute the sqrt  of 3 .. and then multiply that answer times the variable x." ] research PEDMAS

• 2 months ago

√(3x) = (x - 6)

3x = x^2 - 12x + 36

x^2 - 15x + 36 = 0

x^2 - 12x - 3x + 36 = 0

x(x - 12) - 3(x - 12) = 0

(x - 3)(x - 12) = 0

Solutions:

x = 3

x = 12