The ‘sum and square’ problem is a classic math problem that tests the ability to calculate a given number when the sum of the number and its square is known. In this article, we will explore the problem, and provide a step-by-step guide on how to calculate the unknown value.

## Solving the ‘Sum and Square’ Problem

The ‘sum and square’ problem involves finding the value of an unknown number when the sum of the number and its square is known. In this example, the sum of the number and its square is 90.

In order to solve this problem, we need to use the quadratic equation. This equation is used to solve equations of the form ax2 + bx + c = 0, where a, b and c are known values. In this case, a = 1, b = 0 and c = -90.

## Finding the Unknown Value

Using the quadratic equation, we can calculate the unknown value of x. The equation is x = (-b ± √b2 – 4ac) / 2a. Plugging in the values of a, b and c, we get x = ± √90.

As √90 is not a whole number, we need to use the quadratic formula to calculate the two possible solutions to the equation. The two solutions are x = ±9.95.

Therefore, the unknown value is either 9 or -9.95.

In conclusion, the ‘sum and square’ problem is a classic math problem that can be solved using the quadratic equation. By using the equation and plugging in the known values, we can find the unknown value of x. In this case, the unknown value is either 9 or -9.95.

In this mathematical problem, the task is to determine the number given that the sum of the square of the number and the number itself is equal to 90. To solve this problem, we can use the quadratic formula by setting the equation to 0 and determining the two possible solutions. The equation is x2 + x – 90 = 0, and here we apply the quadratic formula.

The Quadratic Formula is: x = [-b ± √(b2 – 4ac)]/2a

In this problem, we have a = 1, b = 1, and c = -90. When we plug these values into the quadratic formula, we have:

x = (-1 ± √(1 + 360))/2

Next, we simplify the equation by subtracting 1 from both sides, resulting in:

x = (-1 ± √361)/2

After simplification, we are left with the final equation of:

x = (-1 ± 19)/2

Using the positive root of the equation and plugging it into our original equation, we have:

x = (19 + 19)/2

Therefore, the value of the number is 19.