Question

The sum of twice the square of a number and 7 times the number equals 15.what is the number

Answer 1

Hey here is your answer

Answer 2

Concept: A quadratic equation is any equation that can be rewritten in standard form as $ax^{2} +bx +c =0$ in algebra where x is an unknown and a, b, and c are known numbers, and $a \neq 0$  because  when a = 0, the equation is linear rather than quadratic.

Given: The sum of twice a number's square and seven times the number equals 15.

To find: the number

Solution:

Let us suppose the number as x.

square of a number means $x^{2}$

twice the square of a number means $2x^{2}$

7 times the number means 7x

Now, according to question,

$2x^{2} + 7x = 15$

$2x^{2} +7x - 15 = 0$

Now, splitting the middle term, we get

$2x^{2} + 10x -3x - 15 = 0\\(2x^{2} + 10x) - (3x +15) = 0\\2x(x + 5) - 3(x + 5) = 0\\(x + 5) (2x -3) = 0\\(x + 5) = 0 and (2x - 3) = 0\\x = -5 \\and \\x = \frac{3}{2}$

Hence, the number is -5 or 3/2.

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