#### Question

The sum of a number and its square is 63/4. Find the numbers.

#### Solution

Let the number be x.

Given that the sum of x and its square = 63/4

⇒ x + 𝑥^{2} = 63/4

⇒ 4x + 4x^{2} - 63 = 0

⇒ 4x^{2} + 4x - 63 = 0

⇒ 4x^{2} + 4x - 63 = 0 ....................(i)

The value of x can be found by the formula

`x=(-b+-sqrt(b^2-4ac))/(2a)`

⇒ here a = 4, b = 4 and c = -63 from (i)

`x=(-4+-sqrt(16-4xx4xx-63))/(2xx4)`

`=(-4+-sqrt(16+16xx63))/(2xx4)`

`x=(-4+-sqrt(16+1008))/8`

Therefore,

`x=(-4+sqrt(16+1008))/8=7/2`

Or

`x=(-4-sqrt(16+1008))/8=-9/2`

∴ The values of x i. e. , the numbers is 7/2 , -9/2.

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Is there an error in this question or solution?

Solution The Sum of a Number and Its Square is 63/4. Find the Numbers Concept: Solutions of Quadratic Equations by Factorization.