Solving Quadratic Equations
The equation in the image is a quadratic equation. It reads: -m² - 7m - 4 = -2m².
To solve for m, we should first simplify and rearrange the equation to standard quadratic form ax² + bx + c = 0. We can start by adding 2m² to both sides to combine like terms:
-m² + 2m² - 7m - 4 = 0,
which simplifies to:
m² - 7m - 4 = 0.
Now, we have a standard quadratic equation that we can solve by factoring, completing the square, or using the quadratic formula. This equation doesn't easily factor, so let's use the quadratic formula:
m = [-b ± sqrt(b² - 4ac)] / (2a),
where a = 1, b = -7, and c = -4.
Plugging in these values:
m = [-(-7) ± sqrt((-7)² - 4 * 1 * (-4))] / (2 * 1),
m = [7 ± sqrt(49 + 16)] / 2,
m = [7 ± sqrt(65)] / 2.
So the solutions for m are:
m = (7 + sqrt(65)) / 2 and m = (7 - sqrt(65)) / 2.
