Question

2(х-6)=0.25x(8x-48)-12

Answer 1

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Answer 2

To solve the equation 2(x - 6) = 0.25x(8x - 48) - 12, follow these steps:

1. Start by distributing the constants on the right side of the equation:

2(x - 6) = 0.25x(8x - 48) - 12

2x - 12 = 2x(x - 6) - 12

2. Expand the terms on the right side of the equation by multiplying 0.25x with each term inside the parentheses:

2x - 12 = 2x * x - 2x * 6 - 12

2x - 12 = 2x^2 - 12x - 12

3. Now, move all the terms to one side of the equation and set it equal to zero:

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

4. Combine like terms:

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

2x^2 - 10x - 12 = 0

5. Divide the entire equation by 2 to simplify it:

x^2 - 5x - 6 = 0

6. Now, factor the quadratic equation:

(x - 6)(x + 1) = 0

7. Set each factor equal to zero and solve for x:

x - 6 = 0 or x + 1 = 0

8. Solve for x in each equation:

x = 6 or x = -1

So, the solutions to the equation are x = 6 and x = -1.