solve 2x^2-25x=3x^2-8x-6

Question

please show me steps and the two solutions

Answer 1

2x² - 25x = 3x² - 8x - 6

What we need to do is move all the pieces to one side of the equals sign, so that the problem equals 0. So we subtract 2x2 and add 25x to both sides:

0 = x² + 17x - 6

This doesn't look like it will factor out evenly, so let's use the quadratic formula:

(-b ± √(b² - 4ac)) / 2a

 

x = (-17 ± √(17² - 4 * 1 * -6)) / (2 * 1)

x = (-17 ± √(289 + 24)) / 2

x = (-17 ± √313) / 2

x = (-17 + √313) / 2, or (-17 - √313) / 2

 

The problem is that square root 313. That's as far as we can go if we want to be completely accurate. Otherwise we're going to have to round off that root:

x ≅ (-17 + 17.691) / 2, or (-17 - 17.691) / 2

x ≅ ^0.691/₂, or -^34.691/₂

x ≅ 0.3455 or -17.3455

Answer 2

You must do some work, called "combining LIKE TERMS" so that you get all terms on one side of the equation.

Then you might be able to factor the quadratic and thus solve it; otherwise, try the quadratic formula.

 

There's nothing especially difficult about this task; you must simply do what everybody in the world will do to solve a quadratic.