Question

Solve by using quadratic formula 8x2+10x=-1

Answer 1

`\displaystyle (-5 \pm√(17) )/(8)`

Explanation:

The quadratic formula is a way of finding all solutions to a quadratic equation.

What is The Quadratic Formula?

The quadratic formula is long and complicated, but it is important to memorize.

• 
  `\displaystyle (-b\pm √(b^2-4ac) )/(2a)`

The constants a, b, and c are the coefficients of the quadratic. The coefficient of x² is a, the coefficient of x is b, and the constant is c. However, this is only true when the equation is equal to zero. Currently, the equation given cannot be used because it is set equal to -1 instead of 0. To solve this, we will have to manipulate the equation slightly.

Solving the Quadratic Formula

Firstly, we need to make the equation set equal to 0. To do this, we can add 1 to both sides.

• 8x² + 10x + 1 = 0

This means that a = 8, b = 10, and c = 1. Now, we can plug these into the formula.

• 
  `\displaystyle (-10\pm√(10^2-(4*8*1)) )/(2*8)`

Then, we can simplify the equation through a series of steps.

• 
  `\displaystyle (-10\pm√(100-32) )/(16)`
• 
  `\displaystyle (-10\pm√(68) )/(16)`

Next, we can simplify the radical.

• 
  `\displaystyle (-10\pm2√(17) )/(16)`

Finally, simplify the denominator.

• 
  `\displaystyle (-5\pm√(17) )/(8)`

This gives us the final answer, which is the 2 possible x-values for the given equation.