How do you solve using the quadratic formula #6x^2 - 6x = x + 9#?

Question

Genesis Allen · Accepted Answer

Rewrite #6x^2-6x = x+9#
into the standard #ax^2+bx+c=0# form: #6x^2-7x-9=0# The quadratic formula for roots is
#x = (-b+-sqrt(b^2-4ac))/(2a)# with the given example
#x= (7+-sqrt(49+216))/12# #= (7+-sqrt(265))/12#

Eva Abramson · Answer

undefined To solve the equation 6x^2 - 6x = x + 9 using the quadratic formula:

1. Rearrange the equation to set it equal to zero: 6x^2 - 6x - x - 9 = 0.
2. Combine like terms: 6x^2 - 7x - 9 = 0.
3. Identify the coefficients: a = 6, b = -7, and c = -9.
4. Apply the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
5. Substitute the coefficients into the formula: x = (7 ± √((-7)^2 - 4 * 6 * -9)) / (2 * 6).
6. Simplify inside the square root: x = (7 ± √(49 + 216)) / 12.
7. Further simplify inside the square root: x = (7 ± √265) / 12.
8. Evaluate both roots: x₁ = (7 + √265) / 12 and x₂ = (7 - √265) / 12.