#### Question

If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.

#### Solution

Let the integer be ‘x’

Given that if an integer is added to its square, the sum is 90.

⇒ 𝑥 + 𝑥^{2} = 90

⇒ 𝑥 + 𝑥^{2} − 90 = 0

⇒ 𝑥^{2} + 10𝑥 - 9𝑥 - 90 = 0

⇒ 𝑥(𝑥 + 10) - 9(𝑥 + 10) = 0

⇒ x = -10 or x = 9

∴ The value of an integer are -10 or 9.

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#### APPEARS IN

Solution If an Integer is Added to Its Square, the Sum is 90. Find the Integer with the Help of Quadratic Equation. Concept: Solutions of Quadratic Equations by Factorization.