Question

Use the quadratic formula to solve the equation. $$8 m^{2}+6 m-1=0$$

Short answer

The solutions to the quadratic equation are \(m = \frac{-3 + \sqrt{10}}{4}\) and \(m = \frac{-3 - \sqrt{10}}{4}\).

Step-by-step solution

Identify the coefficients a, b, and c

In the given quadratic equation \(8m^2 + 6m - 1 = 0\), the coefficient of \(m^2\) (term with power 2) is 'a', the coefficient of 'm' (term with power 1) is 'b' and the constant term is 'c'. So, \(a = 8\), \(b = 6\), and \(c = -1\).

Apply the Quadratic Formula

The quadratic formula is \(-b \pm \sqrt{b^2 - 4ac} \div 2a\). Insert the identified values into the formula to get: \(-6 \pm \sqrt{6^2 - 4*8*(-1)} \div 2*8\)

Simplify the expressions

Calculate the value inside the square root, simplify the expressions and solve for the two roots 'm'. After simplifying, we get \(m = \frac{-3 \pm \sqrt{10}}{4}\).