Please show all work:
1)find the integers whose square is 36 more than 5 times itself
2) If x² is added to 7x, the sum is -12.What are possible values of x?
3)The area of a rectangle is 84 square inches. The length is 5 inches more than the width.Find the rectangle's length.
4) The area of a rectangle is 40 square meters. The width is 6 meters less than the length.Find the rectangle's width and length.
As was gently suggested previously, it's really you who needs to "show all work". We already know how to do this stuff.
The following should help in getting you started:
"Integers" means "the whole numbers and their negatives". Pick a variable to stand for "the integer". Then translate "the square of the integer", "five more than the integer", and "thirty-six more than (five more than the integer)" into algebraic expressions. Use the "is" to create the equation, and then solve the quadratic equation.
Create the expression representing the sum. Set the sum equal to the given value. Solve the quadratic equation.
Since the length is defined in terms of the width, pick a variable for the width and then create an expression, in terms of this variable, for the length. Plug these into the formula for the area A of a rectangle with length L and width w. Also plug in the given value for the area A. Solve the resulting quadratic equation.
This one works just like exercise (3).