Question

6a^2-(a+2)^2=-4(a-4)

Answer 1

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Answer 2

To solve the equation, let's first simplify both sides and then find the value of 'a':

Step 1: Expand the terms on both sides of the equation.

On the left side: 6a^2 - (a + 2)^2 = 6a^2 - (a^2 + 4a + 4)

On the right side: -4(a - 4) = -4a + 16

Step 2: Now, combine like terms on both sides of the equation.

6a^2 - (a^2 + 4a + 4) = -4a + 16

Step 3: Eliminate the parentheses on the left side by distributing the negative sign inside the parentheses.

6a^2 - a^2 - 4a - 4 = -4a + 16

Step 4: Combine like terms again.

5a^2 - 4a - 4 = -4a + 16

Step 5: Move all the terms to one side of the equation.

5a^2 - 4a - 4 + 4a - 16 = 0

Step 6: Simplify the equation further.

5a^2 - 16 = 0

Step 7: Move the constant term to the other side.

5a^2 = 16

Step 8: Isolate 'a' by dividing both sides by 5.

a^2 = 16 / 5

Step 9: Take the square root of both sides to solve for 'a'.

a = ±√(16/5)

Now, let's calculate the value of 'a':

a = ±√(16/5) ≈ ±√(3.2) ≈ ±1.79

Therefore, the solutions for 'a' are approximately a = 1.79 and a = -1.79.