Use the quadratic formula to solve the equation.
8m^2 + 13m - 7 = 0
The quadratic formula is:
m = (-b ± sqrt(b^2 - 4ac)) / 2a
In this equation, a = 8, b = 13, and c = -7. Substitute these values into the quadratic formula and simplify.
m = (-13 ± sqrt(13^2 - 4(8)(-7))) / 2(8)
m = (-13 ± sqrt(169 + 224)) / 16
m = (-13 ± sqrt(393)) / 16
Therefore, the solutions are:
m ≈ -0.893 or m ≈ 0.68
To solve the quadratic equation 8m^2 + 13m - 7 = 0 using the quadratic formula, we first need to identify the coefficients a, b, and c.
The quadratic equation is in the form ax^2 + bx + c = 0.
In this case, a = 8, b = 13, and c = -7.
The quadratic formula is given as:
x = (-b ± √(b^2 - 4ac)) / (2a)
Using the given coefficients, we can substitute them into the quadratic formula:
m = (-13 ± √(13^2 - 4 * 8 * (-7))) / (2 * 8)
Simplifying this equation further:
m = (-13 ± √(169 + 224)) / 16
m = (-13 ± √(393)) / 16
Now, let's find the values of m by calculating separately for each case:
m = (-13 + √(393)) / 16
m = (-13 + √393) / 16
m = (-13 - √(393)) / 16
m = (-13 - √393) / 16
Therefore, the solutions to the quadratic equation 8m^2 + 13m - 7 = 0 using the quadratic formula are:
m = (-13 + √393) / 16 and m = (-13 - √393) / 16.
To solve the given quadratic equation using the quadratic formula, we can follow these steps:
1. Write down the quadratic equation in the form: ax^2 + bx + c = 0
In this case, the equation is: 8m^2 + 13m - 7 = 0
2. Identify the values of a, b, and c from the quadratic equation.
In this case, a = 8, b = 13, and c = -7.
3. Substitute the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
4. Plug in the values into the quadratic formula and simplify the equation.
x = (-13 ± √(13^2 - 4 * 8 * -7)) / (2 * 8)
x = (-13 ± √(169 + 224)) / 16
x = (-13 ± √393) / 16
5. Simplify the square root (√393) if possible.
√393 is an irrational number, so we cannot simplify it further.
6. Write down the two solutions for the quadratic equation.
x1 = (-13 + √393) / 16
x2 = (-13 - √393) / 16
Therefore, the solutions to the given quadratic equation are:
x1 ≈ 0.518
x2 ≈ -1.393