How do you solve the equation $6g + 8 = 9g - 25$?

Question

$6g+8=9g-25$

Can you simply solve for $g$? I'm having trouble with the steps.

Answer 1

we have to solve $$6g+8=9g-25$$ adding $25$ on both sides we get $$6g+33=9g$$ substracting $6g$ this gives $$33=3g$$ and dividing by $3$ and you have the answer.

Answer 2

This is one of the toughest questions I have seen on this site, but here are some steps that might lead to the solution.

We start with the original equation $$6g + 8 = 9g - 25$$ We take the square on both sides to get $${(6g + 8)}^2 = {(9g - 25)}^2$$ Expanding both sides, we get $$36g^2 + 96g + 64 = 81g^2 - 450g + 625$$Subtracting $81g^2 - 450g + 625$ from both sides leaves $$-45g^2 + 546g - 561 = 0$$

This is a quadratic equation, so we can use the famous Quadratic formula to get the solutions: $$ g = \frac{-546 \pm \sqrt{{546}^2 - 4 \cdot -45 \cdot -561} }{2 \cdot -45} $$ which simplifies to $$ g = \frac{546 \mp \sqrt{197136} }{90} $$

Now, the square root of 197136 is 444, so this leaves us with $$ g = \frac{546 \mp 444 }{90} $$ so $g$ is either $\frac{102}{90}$ or $\frac{990}{90}$. When you plug both values into the original equation, you will see which one is the real solution.