6а²-(а+2)²=-4(а-4)
To solve the equation \( 6a^2 - (a + 2)^2 = -4(a - 4) \), let's start by simplifying both sides step by step.
Step 1: Expand the squared term and the right side:
Expand \((a + 2)^2\): \[ (a + 2)^2 = a^2 + 4a + 4 \]
Expand \(-4(a - 4)\): \[ -4(a - 4) = -4a + 16 \]
Step 2: Substitute these expansions into the equation:
The equation now looks like this: \[ 6a^2 - (a^2 + 4a + 4) = -4a + 16 \]
Step 3: Simplify the left side:
Combine the terms on the left: \[ 6a^2 - a^2 - 4a - 4 = -4a + 16 \] \[ 5a^2 - 4a - 4 = -4a + 16 \]
Step 4: Move all terms to one side of the equation:
Add \(4a\) to both sides: \[ 5a^2 - 4 = 16 \]
Next, subtract \(16\) from both sides: \[ 5a^2 - 4 - 16 = 0 \] \[ 5a^2 - 20 = 0 \]
Step 5: Simplify further:
Add \(20\) to both sides: \[ 5a^2 = 20 \]
Divide by \(5\): \[ a^2 = 4 \]
Step 6: Solve for \(a\):
Take the square root of both sides: \[ a = 2 \quad \text{or} \quad a = -2 \]
Final Answer:
Thus, the solutions to the equation \( 6a^2 - (a + 2)^2 = -4(a - 4) \) are: \[ a = 2 \quad \text{and} \quad a = -2 \]
