How do you solve #3x^2 – 2x = 15x – 10#?

Question

Eva Adamson · Accepted Answer

#x=color(red)(5), color(blue)(2/3)#

Put all terms together on one side.

#3x^2-2x-15x+10=0"#

Mix similar terms together.

#3x^2-17x+10=0# is a quadratic equation in the form #ax^2+bx+c#, where #a=3, b=-17, c=10#.

To solve the equation, apply the quadratic formula.

#x=(-b+-sqrt(b^2-4ac))/(2a)#

Replace the values found in the equation.

#x=(-(-17)+-sqrt((-17)^2-4*3*10))/(2*3)#

Simplify.

#x=(17+-sqrt(289-120))/6#

Simplify.

#x=(17+-sqrt 169)/6#

Simplify.

#x=(17+-13)/6#

Solve for #x#.

#color(red)(x=(17+13)/6)#

#color(red)(x=30/6)#

#color(red)(x=5)#

#color(blue)(x=(17-13)/6)#

#color(blue)(x=4/6)#

Diminish the percentage.

#color(blue)(x=2/3)#

Eli Assouline · Answer

undefined To solve the equation 3x^2 - 2x = 15x - 10, follow these steps:

1. Combine like terms to get the equation in standard quadratic form: 3x^2 - 15x - 2x + 10 = 0.
2. Rearrange the terms: 3x^2 - 17x + 10 = 0.
3. To solve the quadratic equation, you can use factoring, completing the square, or the quadratic formula.
4. Factoring may not be straightforward, so you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 3, b = -17, and c = 10.
5. Plug the values into the formula: x = (17 ± √(17^2 - 4*3*10)) / (2*3).
6. Simplify: x = (17 ± √(289 - 120)) / 6.
7. Further simplify: x = (17 ± √169) / 6.
8. Find the square root of 169: x = (17 ± 13) / 6.
9. Calculate both possible solutions: x1 = (17 + 13) / 6 = 30 / 6 = 5 and x2 = (17 - 13) / 6 = 4 / 6 = 2/3.
10. Therefore, the solutions to the equation are x = 5 and x = 2/3.