Question - Solving Quadratic Equations
mathsolving quadratic equationsquadratic formulastandard quadratic formfactoring quadratic equations
Solution:
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.
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