The sum of a number and its square is 90 Find the number?

Answer 1

Use any letter for the number, for example, x. The equation is:

x + x2 = 90

This should be converted to standard form before proceeding:

x2 + x = 90
x2 + x - 90 = 0

This can easily be factored. You need two numbers (one positive, one negative), whose sum is +1, and whose product is -90.

(x + 10)(x - 9) = 0

This gives you two solutions for x:

x + 10 = 0
x = -10

or:

x - 9 = 0
x = 9

Note: it is quite common for a quadratic equation to have two solutions.

Use any letter for the number, for example, x. The equation is:

x + x2 = 90

This should be converted to standard form before proceeding:

x2 + x = 90
x2 + x - 90 = 0

This can easily be factored. You need two numbers (one positive, one negative), whose sum is +1, and whose product is -90.

(x + 10)(x - 9) = 0

This gives you two solutions for x:

x + 10 = 0
x = -10

or:

x - 9 = 0
x = 9

Note: it is quite common for a quadratic equation to have two solutions.

Use any letter for the number, for example, x. The equation is:

x + x2 = 90

This should be converted to standard form before proceeding:

x2 + x = 90
x2 + x - 90 = 0

This can easily be factored. You need two numbers (one positive, one negative), whose sum is +1, and whose product is -90.

(x + 10)(x - 9) = 0

This gives you two solutions for x:

x + 10 = 0
x = -10

or:

x - 9 = 0
x = 9

Note: it is quite common for a quadratic equation to have two solutions.

Use any letter for the number, for example, x. The equation is:

x + x2 = 90

This should be converted to standard form before proceeding:

x2 + x = 90
x2 + x - 90 = 0

This can easily be factored. You need two numbers (one positive, one negative), whose sum is +1, and whose product is -90.

(x + 10)(x - 9) = 0

This gives you two solutions for x:

x + 10 = 0
x = -10

or:

x - 9 = 0
x = 9

Note: it is quite common for a quadratic equation to have two solutions.

Answer 2

Use any letter for the number, for example, x. The equation is:

x + x2 = 90

This should be converted to standard form before proceeding:

x2 + x = 90
x2 + x - 90 = 0

This can easily be factored. You need two numbers (one positive, one negative), whose sum is +1, and whose product is -90.

(x + 10)(x - 9) = 0

This gives you two solutions for x:

x + 10 = 0
x = -10

or:

x - 9 = 0
x = 9

Note: it is quite common for a quadratic equation to have two solutions.