What are the solutions of the equation x^2-30=x in x=-6,x=-5 x=-6,x=5 x=-5,x=6 x=5,x=6

To solve the equation $x^2 - 30 = x$, we can rearrange the equation to $x^2 - x - 30 = 0$. This is a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a = 1$, $b = -1$, and $c = -30$.<br /><br />We can solve this quadratic equation by factoring. We need to find two numbers whose product is $ac = -30$ and whose sum is $b = -1$. The two numbers that satisfy these conditions are $-6$ and $5$.<br /><br />So, we can factor the quadratic equation as $(x - 6)(x + 5) = 0$.<br /><br />Setting each factor equal to zero gives us the solutions:<br />$x - 6 = 0$ or $x + 5 = 0$<br /><br />Solving for $x$, we get:<br />$x = 6$ or $x = -5$<br /><br />Therefore, the solutions to the equation $x^2 - 30 = x$ are $x = 6$ and $x = -5$.<br /><br />So, the correct answer is $x = -5, x = 6$.