m^2-5m-14=0.
Solve using quadratic formula. Thanks.
m=2, or m=-7
m = (5 ± √(25 - 4(1)(-14))/2
= (5 ± √81)/2
= (5±9)/2
= 7 or -2
To solve the quadratic equation m^2 - 5m - 14 = 0 using the quadratic formula, follow these steps:
1. Identify the coefficients of the equation: a = 1, b = -5, c = -14.
2. Substitute the values into the quadratic formula: m = (-b ± √(b^2 - 4ac)) / (2a).
3. Plug the values into the quadratic formula: m = (-(-5) ± √((-5)^2 - 4(1)(-14))) / (2(1)).
4. Simplify the equation: m = (5 ± √(25 + 56)) / 2.
5. Further simplify the equation: m = (5 ± √81) / 2.
6. Calculate the square root: m = (5 ± 9) / 2.
7. Solve for the two possible values of m:
m = (5 + 9) / 2 = 14 / 2 = 7,
m = (5 - 9) / 2 = -4 / 2 = -2.
Therefore, the solutions to the quadratic equation m^2 - 5m - 14 = 0 are m = 7 and m = -2.
To solve the quadratic equation m^2 - 5m - 14 = 0 using the quadratic formula, we need to follow these steps:
Step 1: Identify the coefficients a, b, and c in the equation. In this case, a = 1, b = -5, and c = -14.
Step 2: Substitute the values of a, b, and c into the quadratic formula:
m = (-b ± √(b^2 - 4ac)) / (2a)
Step 3: Calculate the discriminant (the expression inside the square root) to determine the nature of the roots. The discriminant is given by the formula Δ = b^2 - 4ac.
In this case, Δ = (-5)^2 - 4(1)(-14) = 25 + 56 = 81.
Step 4: If the discriminant is greater than zero (Δ > 0), there are two real and distinct solutions. If the discriminant is zero (Δ = 0), there is one real and repeated solution. If the discriminant is less than zero (Δ < 0), there are no real solutions, only complex solutions.
In our case, Δ = 81, which is greater than zero, so there will be two distinct real solutions.
Step 5: Apply the quadratic formula to find the values of m:
m = (-(-5) ± √(81)) / (2(1))
m = (5 ± 9) / 2
Using the positive square root of 81:
m1 = (5 + 9) / 2 = 14 / 2 = 7
Using the negative square root of 81:
m2 = (5 - 9) / 2 = -4 / 2 = -2
Therefore, the solutions to the equation m^2 - 5m - 14 = 0 are m1 = 7 and m2 = -2.