Determine whether the values of 10 and 30 are solutions to the quadratic equation (x-27)(x-10)=60

Answer 1

To determine if the values of $10$ and $30$ are solutions to the equation $(x-27)(x-10)=60$, we will substitute each value into the equation and check if the equation holds.

1. Substituting $x=10$: $$(10-27)(10-10)=60$$ This simplifies to: $$(-17)(0)=60$$ This results in: $$0=60$$ This is false. Therefore, $10$ is not a solution.

2. Substituting $x=30$: $$(30-27)(30-10)=60$$ This simplifies to: $$(3)(20)=60$$ This results in: $$60=60$$ This is true. Therefore, $30$ is a solution.

In conclusion, $10$ is not a solution, while $30$ is a solution to the quadratic equation $(x-27)(x-10)=60$.