Question

Use the quadratic formula to find the roots: -2x^2 + 11x = 15​

Answer 1

`x=3,(5)/(2)`

General Formulas and Concepts:

Quadratic Formula:
`x=(-b\pm√(b^2-4ac) )/(2a)`

Standard Form: ax² + bx + c = 0

Order of Operations: BPEMDAS

Explanation:

Step 1: Define

-2x² + 11x = 15

-2x² + 11x - 15 = 0

a = -2, b = 11, c = -15

Step 2: Solve for x

1. Substitute:
   `x=(-11\pm√(11^2-4(-2)(-15)) )/(2(-2))`
2. Exponents:
   `x=(-11\pm√(121-4(-2)(-15)) )/(2(-2))`
3. Multiply:
   `x=(-11\pm√(121-120) )/(-4)`
4. Subtract:
   `x=(-11\pm√(1) )/(-4)`
5. Evaluate:
   `x=(-11\pm1)/(-4)`
6. Simplify:
   `x=3,(5)/(2)`