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Find the smaller value of x that satisfies the equation x^{2} + 7x + 10 = 0

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x^{2} + 7x + 10 = 0

The above equation is a quadratic equation and thus, the sum of root = 7 and product of root = 10.

Hence, we look for two numbers, when multiplied gives us 10 and when added gives us 7.

Let the two numbers be 5 and 2.

Replace the sum of root with the two numbers. That is:

x^{2} + 5x + 2x + 10 = 0

Group the equation into two

(x^{2} + 5x) + (2x + 10) = 0

factorise out the common term in each groupings

x(x + 5) + 2(x + 5) = 0

(x + 2) (x + 5) = 0

x + 2 = 0 and x + 5 = 0

x = -2 and x = -5

Therefore, the smallest value of x is x = -5

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